Normal Value Tables

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索引索引中的页码为英文原书页码，与书中页边标注的页码一致AA．R．E．（asymptotic relative efficiency）（渐近相对效率），112of Cox and Stuart test（Cox 和Stuart检验）, 175, 323of Daniel test（Daniel检验）, 322of Durbin test（Durbin检验）, 394of Frieaman test（Frieaman检验）, 379of Kendall’s tau, 327of Kruskal-Wallis test（Kruskal-Wallis检验）, 287of Mann-Whitney test（Mann-Whitney检验）, 284of median test（中位数检验）, 285, 297of paired t test（配对t检验）, 364of Quade test（Quade检验）, 380of quantile test vs. one-sample t test（分位数检验对一样本t检验）, 148of rank test for slope（斜率的秩检验）, 342of sign test（符号检验）, 363of sign test vs. t test（符号检验vs. t检验）, 164，175of sign test vs. Wilcoxon signed ranks test（符号检验vs. Wilcoxon符号秩检验）,164, 175 of Spearman’s rho,327of squared ranks test（平方秩检验）, 309of two-sample t test（两样本t检验）, 284of Wilcoxon signed ranks test（Wilcoxon符号秩检验）, 363acceptance region（接受域）, 98aligned-rank methods（秩排列方法）,384, 385alternative hypothesis（备择假设）,95alternatives, ordered（备择的，次序的）, 297analysis of covariance（方差分析）, 297analysis of covariance,one-way（方差分析,一种方式）, 222, 297approximate confidence interval for μ（μ的近似置信区间）, 85approximation formulas for tolerance limits（容忍限逼近公式）, 151, 155 approximation, normal（逼近，正态）:to binomial distribution（二项分布）, 58to sum of ranks（秩和）, 58approximations to chi-squared distribution（χ2分布近）, 62asymptotic relative efficiency, (see also A. R. E)（渐近相对效率）, 112asymptotically distribution-free methods（渐近分布自由方法）, 117Bbiased estimators for σ, 85 σ的有偏估计量biased test, 108 有偏检验binomial coefficient, 9, 11 二项系数binomial distribution, 28 二项分布mean and variance in, 49 均值和方差normal approximation to, 58 正态逼近tables of the, 513-524 表格tests based on the, 123 基于…的检验binomial expansion, 11 二项展开binomial test, 104, 124 二项检验power of, 127 功效bioassay, 119 生物鉴定bivariate random variable, 72 二维随机变量block design, incomplete, 387 区组设计，不完全的randomized complete, 251, 368 完全随机化blocks, multiple comparisons with complete, 371, 375 区组, 完全多重比较bootstrap, 349 bootstrapbootstrap method of estimation, 86 估计的bootstrap方法censored data, 297 删失数据censored sample, 155, 285 删失样本central limit theorem, 57, 85 中心极限定理centroid, 36 重心chi-squared approximation to Kruskal-Wallis test, 295 χ2近似Kruskal-Wallis检验chi-squared approximation distribution function, 54, 59 分布函数的χ2逼近approximations to, 62 逼近到…tables, 512 表格chi-squared goodness-of-fit test, 239, 240, 429, 430, 442, 443 χ2拟合优度检验chi-squared random variables, sum of, 62 χ2随机变量，和chi-squared test: χ2检验for differences in probabilities, 180, 199 概率差异with fixed marginal totals, 209 固定边缘总和for independence, 204 独立性circular distributions, 285, 364 圆周分布cluster analysisi, 419 聚类分析Cochran test, 250 Cochran检验Cochran’s criteria for small expected values, 202 对小期望值的Cochran准则confidence, 83 置信multinomial, 9, 12 多项式coefficient of concordance, Kendall’s, 328, 380 一致性系数，Kendall’s comparisons, multiple: 对比，多重with complete blocks, 371, 375 完全区组incomplete blocks, 390 不完全区组with independent sample, 290, 297, 398 独立样本in test for variances, 304 方差检验complete block design, randomized, 368 完全区组设计，随机化completely randomized design,222 完全随机化设计composite hypothesis, 97 复合假设computer simulation to find null distribution, 446, 447 计算机模拟求零假设分布concordance between blocked rankings, 385 区组秩间的一致性condorance, Kendall’s coefficient of, 328, 382 一致性, Kendall 系数concordant pairs, 319 不和谐配对conditional probability, 17, 23, 24 条件概率conditional probability function, 29 条件概率函数confidence band for a distribution function,438 分布函数置信界confidence coefficient, 83, 114, 129 置信系数for the difference between two means, 281 两均值差异for a mean, parametric, 149 均值，参数for the median difference, 360 中位差异for μ, approximate, 85 对于μ, 逼近for a probability or population proportion, 130 对于概率或总体比例exact tables for, 525-536 精确表格for a quantile, 135, 143 分位数one-sided, 153 单边for a slope, 335 斜率conservative test, 113 保守检验consistent, 117 相合的consisitent sequence of tests, 106, 108, 160 检验的相合序列consistent, sign test, 163 相合,符号检验contingency coefficient 列联系数:Cramér’s, 229 CramérPearson’s, 231 PearsonContingency table, 166, 179, 199, 292 列联表fourfold, 180 四重的multi-dimenional, 215 多维的r×c, 199 r×c维three-way, 214 三种方式的two-way, 214 两种方式的continuity correction, 126, 127, 135, 138, 159, 190, 192, 194, 195 连续修正in Kendall’s tau, 322 Kendall’s tauin Mann-Whitney test, 274, 275 Mann-Whitney 检验in Wilcoxon signed ranks test, 359 Wilcoxon符号秩检验continuous distribution function, 53 连续分布函数continuous random variable, 52, 53 连续型随机变量control, sign test for comparing several treatments with a, 175 控制，几种处理比较的符号检验convenience sample, 69 方便样本correction for continuity, 126, 127, 135, 138, 159, 190, 192, 194, 195 连续修正correction, Sheppard’s, 248 修正，Sheppard correlation: 相关性quick test for, 196 快速检验rank, 312 秩sign test for, 172 符号检验correlation coefficient: 相关系数Kendall’s partial,327 Kendall 偏Kendall’s rank, 318, 319, 325, 326 Kendall 秩Pearson’s product moment, 313,318 Pearson 乘积矩Spearman’s rank, 314, 325, 326 Spearmn秩correlation coefficient between two random variables, 43 两随机变量的相关系数correlation test: 相关性检验Kendall’s rank, 175, 321 Kendall秩Spearman’s rank, 175, 316 Spearma秩counting rules, 5 计数法则covariance, 39 协方差analysis of, 297 分析of two random variables, 41, 42, 46 两随机变量of two ranks, 45 两秩Cox and Stuart test for trend, 169, 170 Cox 和Stuart趋势检验A.R. E. of, 175Cramér’s coefficient, 230, 234 Cramér系数Cramér’s contingency coefficient, 229 Cramér列联系数Cramér’s-von Mises goodness-of –fit test, 441 Cramér’s-von Mises拟合优度检验Cramér’s-von Mises two-sample test, 463 Cramér’s-von Mises两样本检验tables for, 464 表格critical region, 97, 98, 101 临界区域size of, 100 大小curves, survival, 119 曲线, 生存Daniel’s test for trend, 323 Daniel趋势检验decile, 33, 34 十分位数(的)decision rule, 98 决策法则degrees of freedom, 59 自由度dependence, measure of, 227 相依，度量design: 设计completely randomized, 222 完全随机化experimental, 419 经验incomplete block, 387 不完全区组randomized complete block, 368 随机化完全区组deviates, random normal, 404 偏离，正态随机difference between two means, confidence interval for the, 281 两均值差异，置信区间difference, confidence interval for the median, 360 差异，中位数置信区间discordant pairs, 319 不和谐配对discrete distribution function, 52 离散分布函数discrete random variable, 52 离散型随机变量discrete uniform distribution, 28, 437 离散均匀分布discriminant analysis, 119, 419 判别分析dispersion, sign test for trends in, 175 散布，趋势的符号检验distribution: 分布binomial, 27 二项discrete uniform, 28 离散均匀exponential, 447 指数hypergeometric, 30 超几何分布lognormal, 453 对数正态分布null, 99 零假设uniform, 433 均匀distribution-free, 114 分布自由distribution-free methods, asymptoticall, 117 分布自由方法，渐近的distribution function, 26 分布函数chi-squared, 54, 59 χ2confidence band for, 438 置信界continuous, 53 连续discrete, 52 离散empirical, 79, 428 经验joint, 29 联合normal, 54, 55 正态of order statistics, 146, 147, 153 次序统计量sample, 79, 80 样本distributions with heavytails, 116, 148, 164 重尾分布distributions with light tails, 116, 164 轻尾分布dose-response curves, 349 剂量响应曲线Durbin test, 387, 388 Durbin检验efficiency of, 394 效率efficiency, 106 效率asymptotic, 112 渐近的of the Durbin test,394 Durbin检验of the Friedman test, 379 Friedman检验of the paired t-test, 364 配对t检验的relative, 110, 111, 112 相关的of the sign test, 364 符号检验of the Smirnov test, 465 Smirnov检验of the Wilcoxon test, 364 Wilcoxon检验empirical distribution function, 79, 428 经验分布函数empirical survival function, 89 经验生存函数empty set, 14 空集error: 误差standard, 85, 88 标准type Ⅰ, 98 Ⅰ类typeⅡ,98, 99 Ⅱ类estimate: 估计interval, 83 区间point, 83 点of the standard deviation, 443 标准差estimation, 79, 88 估计of parameters in chi-squared goodness-of-fit test, 243, 245, 249 参数χ2拟合度估计estimator, 79, 81 估计量of population mean, 115 样本均值of population standard deviation, 115 样本标准差unbiased, 74 无偏for μ, 84 μfor σ2, 85 σ2 event, 7, 14 事件probability of, 14 概率sure, 14 必然事件events, independent, 18, 19 事件，独立joint, 17 联合mutually exclusive, 18, 19 互不相容exact test, Fisher’s, 188, 213 精确检验，Fisher exclusive, mutually, 14 不相容，相互expected normal scores, 404 期望正态得分expected value, 35, 39 期望(值) expected values, small: 期望(值)，小in contingency tables, 201, 220 列联表in goodness-of-fit test, 241, 249 拟合优度检验experiment, 6, 69 试验experimental design, 419 试验设计experiments, independent, 15, 19, 20 试验，独立exponential distribution, 447 指数分布Lilliefors test for the, 448 Lilliefors检验extension of the median test, 224 中位数检验的扩展F-distribution: F分布in Friedman test, 370 Friedman检验in incomplete block analysis, 389 不完全区组分析in Quade test, 374 Quade检验table of the, 562-571 表格F statistic, 297, 300 F统计量computed on scores, 312 得分计算F test, 297, 300 F检验for equal variances, 308, 309 等方差for randomized complete blocks, 379 随机完全区组factorial notation, 8 阶乘记号families of distributions, goodness-of-fit tests for, 442 分布族，拟合优度检验Fisher’s: Fisherexact test, 188, 213 精确检验least significant difference, 296 最小显著差异LSD procedure on ranks, 379method of randomization,407 随机化方法four-fold contingency table, 180, 233 四重列联表freedom, degrees of, 59 自由，度Friedman test, 367, 369 Friedman检验efficiency of, 379 效率extension of, 383 推广function: 函数distribution, 26 分布powder, 163 功效probability, of a random variable, 25 概率, 随机变量probability, on a sample space, 15 概率,样本空间random, 80 随机step, 52 阶梯survival, 80 生存gamma coefficient, 320 gamma 系数goodness-of-fit test: 拟合优度chi-squared, 239, 240 χ2Cramér-von Mises, 441 Cramér-von Mises kolmgorov, 428,430, 435 Kolmgorov goodness-of-fit tests for families of distributions,442 分布族拟合优度检验grand median, 218 全中位数heavy tails, distributions with, 116, 148, 164 重尾，分布Hodges-Lahman estimate of shift, 282, 361 Hodges-Lahman 漂移估计hypergeometric distribution, 30, 188, 191 超几何分布mean of, 188, 191 均值standard deviation of, 188, 191 标准差hypothesis: 假设alternative, 95 备择的composite, 97 复合的null, 95 零假设simple, 97 简单testing, 95 检验tests, properties of, 106 检验，性质incomplete block design, 368, 387 不完全区组设计incomplete block, multiple comparisons, 390 不完全区组, 多重比较independence, the chi-squared test for, 204 独立，χ2检验independent: 独立events, 18, 19 事件experiments, 15, 19, 20 试验random variables, 31, 46, 72 随机变量samples, multiple comparisons with, 290, 296, 398 样本，多重比较samples, randomization test for two, 409 样本，随机化检验inference, statistical, 68 推断，统计的interaction: 交互rank transformation test for, 419 秩变换检验test for, 384 检验intercept, 333 截距Internet websites, v 因特网，网址interquartile range, 37 四分位数极差interval, confidence, 83 区间，置信interval estimate, 83, 129 区间估计interval scale of measurement, 74 测量的区间尺度joint distribution function, 28, 29 联合分布函数joint event, 17 联合事件joint probability function, 28 联合概率函数Jonckheere-Terpstra test for ordered alternatives, 325 Jonckheere-Terpstra顺序备择检验Kaplan-Meier estimator, 89 Kaplan-Meier估计量Kendall’s: Kendall coefficient of concordance, 328 一致性系数partial correlation coefficient, 327 偏相关系数rank correlation test, 175, 321 秩相关检验tau, 318, 319, 325, 326, 335exact tables, 545-546 精确表tau, A. R. E. of, 327 tautau for ordered alternatives,381 顺序备择tau Klotz test, 401 Klotz检验Kolmogorov goodness-of-fit test, 428, 430 Kolmogorov 拟合优度检验exact tables, 549 精确表Kolmogorov goodness-of-fit test for discrete distributions, 435离散分布的Kolmogorov拟合优度检验Kolmogorov-Smirnov tests, 428 Kolmogorov-Smirnov检验Kruskal-Wallis test, 288 Kruskal-Wallis检验exact tables for, 541 精确表least significant difference, Fisher’s, 296 最小显著差异, Fisher’s least squares estimates, 334 最小二乘估计least squares method, 333 最小二乘方法Let’s make a deal, 66 让我们和妥协level of significance, 99 显著水平life testing, 148 寿命检验light tails, distributions with, 116, 164 轻尾，分布likelihood ratio statistic, 258 似然比统计量likelihood ratio test, 259 似然比检验Liliefors test for the exponential distribution, 448 指数分布的Liliefors检验table, 551 表格Liliefors test for normality, 443 Liliefors 正态性检验tables, 551 表格limits, tolerance, 150 极限，容忍linear regression, 333 线性回归location estimates, robust, 362 位置估计，稳健location measure of, 36 位置度量loglinear models, 215, 259 对数线性模型lognormal distribution, 453 对数正态分布longitudinal studies, 119 纵向研究lottery game, Texas Lotto, 66 彩票游戏，Texas Lotto lower-tailed test, 98 左边检验Mann-Whitney test, 103, 203, 271 Mann-Whitney检验tables, 538-540 表格Mantel-Haenszel test, 192 Mantel-Haenszel检验marginal totals, chi-squared test with fixed, 209 边缘和，固定的χ2检验matched pairs,350 配对randomization test for, 412 随机化检验McNemar test, 166, 180, 252, 255, 256 McNemar检验compared with paired t test, 178 与配对t检验比较mean, 36, 51 均值of hypergeometric distribution, 188, 191 超几何分布population, estimator of, 115 总体，估计量in rank test using scores, 306 得分的秩检验sample, 81, 83 样本of sum of random variables, 39 随机变量和of sum of ranks, 41, 49 秩和and variance in binomial distribution, 49 二项分布的方差means: 均值confidence interval for the difference between two, 281 两差异的置信区间sign test for equal, 160 对相等的符号检验measurement scale, 73 度量尺度interval, 74 区间nominal, 73 名义ordianal, 74 有序的ratio, 75 比率measures of dependence, 227 相依度量median, 33, 34 中位数difference, confidence interval for, 360 差异，置信区间grand, 218 总的sample, 82 样本test, 218, 352, 355 检验comparison with Kruskal-Wallis test,291 与Kruskal-Wallis检验的比较an extension of, 224 一个推广medians, sign test for equal, 160 中位数，对相等的符号检验meta-analysis, 452 无-分析minimum chi-squared method, 243, 245 最小χ2距离方法Minitab, v, 91, 107, 127, 130, 139, 144, 161, 182, 201, 205, 210, 220, 241, 276, 282, 290, 318, 322, 328, 336, 355, 361, 371, 382, 390, 444, 451model, 6 模型models，loglinear,215, 259 模型，对数线性monotonic regression, 344 单调回归Mood test for variances, 309, 312 Mood 方差检验multi-dimensional contingency table, 215 多维列联表multinomial: 多项式的coefficient, 9, 12, 系数distribution, 203, 207, 249 分布proportions, simultaneous confidence intervals for, 133 比例，联合置信区间multiple comparisons: 多重比较complete block design, 371, 375 完全区组设计incomplete blocks design,390 不完全区组设计independent samples, 290,297,398 独立样本in one-way layout, 220,222,252 以一种方式设计variance, 304 方差multiple regression, 419 多元回归multivariate data, randomization test for, 416 多元数据，随机化检验multivariate observations,385 多元观察multivariate random variable, 71, 72 多元随机变量confidence region for, 362, 364 置信区间mutually exclusive, 14 互不相容events, 19 事件NCSS, vnominal scale data, 117, 118 名义尺度数据nominal scale of measurement, 73 测量的名义尺度nonparametric methods, 116 非参数方法nonparametric statistics, 2, 114 非参数统计definition, 118 定义normal approximation: 正态逼近to binomial distribution, 58 二项分布to chi-squared distribution, 62 χ2分布to hypergeometric, 188, 194 超几何in Mann-Whitney test, 301, 302 Mann-Whitney检验to sum of ranks, 58 秩和in Wilcoxon signed ranks test, 301, 302 Wilcoxon秩和检验normal deviates, random, 404 正态偏差，随机normal distribution function, 54, 55 正态分布函数standard, 55 标准正态分布函数tables of, 508-511 标准正态分布函数表normal scores, 396 标准得分expected,404 期望的in matched pairs test, 400 配对检验in one-way layout, 397 以一种方式设计in test for correlation, 403 相关检验in test for variance, 401 方差检验in two-way layout, 403 以两种方式设计normality: 正态Lilliefors test for, 443 Lilliefors正态检验Shapiro-Wilk test for, 450 Shapiro-Wilk检验normalized sample, 443 标准化样本null distribution, 99 零假设分布null hypothesis,96 零假设one-sample case, 350 一样本情形one-sample t test, 363, 418 一样本t 检验one-tailed test,98 单边检验one-to-one correspondence, 52 一一对应one-way analysis of variance, 222, 297 一种方式的方差分析one-way layout, 227 一种方式的设计order statistic of rank k, 77, 82 秩的次序统计量order statistics, 143 次序统计量distribution function of,146, 147, 153 分布函数ordered alternatives, 297, 385 有序备择Jonckheere-Terpstra test for, 325 Jonckheere-Terpstra检验Page test for, 380 Page检验ordered categories, analysis of contingency table with, 292 有序分类，列联表分析ordered observation, 77 次序观察ordered random sample, 77 次序随机样本ordinal data, 117, 118, 271, 272 有序数据ordinal scale of measurement, 74 测量的顺序尺度outcomes, 6 结果outliers, 117, 284, 297 离群值p-value, 101 p-值Page test for ordered alternatives, 380 顺序备择的Page检验paired t test, 363 配对t检验efficiency of,364 效率McNemar test compared with, 178 McNemar检验的比较parallelism of two regression lines, 364 两回归直线的平行parameter estimation, 88 参数估计parametric confidence interval for mean, 149 均值的参数置信区间parametric methods, 115 参数方法parametric statistics, 2, 114 参数统计partial correlation coefficient: 偏相关系数Kendall’s, 327 Kendall’Spearman’s, 328 SpearmanPASS, v, 107Pearson product moment correlation coefficient, 313 Pearson乘积矩相关系数Pearson’s Pearsoncontingency coefficient, 231 列联系数mean-square contingency coefficient, 231 均方列联系数product moment correlation coefficient, 313, 318 乘积矩相关系数percentile, 33, 34 百分位点phi coefficient, 234, 239 phi系数Pitman’s efficiency, 112 Pitman有效性point estimate, 83 点估计point in the sample space, 13 样本空间中的点population, 68, 69 总体sampled, 69, 70 抽样target, 69, 70 目标power, 3, 100, 106, 116 功效of the binomial test, 127 二项检验function, 106, 163 函数probabilities, chi-squared test for differences in, 180, 199 概率，差异的χ2检验probability, 5, 13 概率conditional, 17, 23 条件的confidence interval for, 130 置信区间of the event, 14 事件function, 15 函数conditional, 29 条件的joint, 28 联合of the point, 14 点的sample, 69 样本properties of random variables, 33 随机变量的性质proportion, confidence interval for population, 130 比例，总体的置信区间Quade test, 367, 373 Quade检验efficiency of, 380 效率power of, 380 功效quantile, 27, 33, 34 分位数confidence interval for, 135, 143 置信区间population, 136 总体sample, 81 样本test, 135, 136, 222 检验A.R.E. vs.one-sample t test, 148 A.R.E. vs.一样本t检验quartile, 33, 34 四分位数random function, 80 随机函数random normal deviates, 404 随机正态偏差random sample, 69, 70, 71 随机样本random variable, 22, 23, 76 随机变量bivariate, 72 二维continuous, 52, 53 连续discrete, 52 离散distribution function of, 26 分布函数multivariate, 71, 72 多元probability function of, 25 概率函数random variables: 随机变量correlation coefficient between two, 43 两随机变量的相关系数covariance of two, 41, 42, 46 两随机变量的协方差independent, 31, 46, 72 独立properties of, 33 性质randomization, Fisher’s method of, 407 随机化，Fisher方法randomization test for two independence samples, 409 独立样本的随机化检验randomized complete block design, 251, 368 随机化完全区组设计randomness, test for, 242 随机，检验range, 37 极差interquartile, 37 四分位数间的rank correlation, 312 秩相关Kendall’s test for, 175, 321 Kendall检验spearman’s test for, 175, 316 Spearman检验rank of an order statistic, 77 次序统计量的秩rank transformation, 417 秩变换ranks: 秩covariance of two, 45 两随机变量的协方差mean of sum of, 41, 49 和的均值ratio scale of measurement, 75 测量的比率尺度region: 域acceptance, 98 接受critical, 97, 98, 101 临界rejection, 98 拒绝regression, 328, 332 回归equation, 332 方程linear, 333 线性monotonic, 344 单调multiple, 419 多元parallelism of two lines, 364 两线平行rejection region, 98 拒绝域relative efficiency, 110, 111, 112 相对效率asymptotic, 112 渐近Resampling Stats, v, 88 重抽样research hypothesis, 95 假设研究rho, Spearman’s, 314, 325, 326, 335 rho, Spearman relationship with Friedman’s test, 382 与Friedman检验的关系robust, 419, 420 稳健location estimates, 362 局部估计methods, 115, 119 方法runs tests, 3 游动检验S-Plus, v, 88, 91, 127, 130, 168, 182189, 193, 201, 205, 210, 241, 276, 290, 318, 322, 355, 371, 432, 444, 449sample, 68, 69 样本censored, 155, 285 删失convenience, 69 方便distribution function, 79, 80 分布函数mean, 81, 83 均值mean, unbiased for μ, 84 均值，对μ无偏median, 82 中位数normalized,443 正则化probability, 69 概率quantile,81 分位数sequential, 362 序贯space, 13 空间point in the, 13 样本空间中的点standard deviation, 83 标准差variance, 81, 83 方差unbiased for σ2, 85 对σ2无偏sampled population, 69, 70 抽样总体SAS, v, 168, 182, 189, 193, 201, 205, 210, 230, 259, 276, 290, 322, 325, 355, 371, 390, 451 scale,measure of, 37 刻度(尺度), 度量scale,tests for, 309, 310 刻度,检验scale, measurement, 73 刻度, 测量scorses, 306 得分expected normal, 404 期望正态F statistic computed on, 312 计算F统计量mean in rank test using, 306 均值的秩检验normal, 396 正态variance in rank test using, 307 方差的秩检验sequential sampling, 362 序贯抽样sequential testing, 285 序贯检验set, empty, 14 集合，空集Shapiro-Wilk test for normality, 450 Shapiro-Wilk正态检验Siegel-Tukey test, 312 Siegel-Tukey检验sign test, 157 符号检验consistent, 163 相合for correlation, 172 相关性efficiency of, 364 效率for equal means, 160 等均值for equal medians, 160 等中位数extension to k samples of, 367 推广到k样本unbiased, 163 无偏variations of, 166, 175 方差vs. t test, A.R.E. of, 164, 175 vs. t检验，A.R.E. vs. Wilcoxon signed ranks test, A.R.E of, 164, 175 vs. Wilcoxonf符号秩检验，A.R.E signed ranks test, Wilcoxon, 352 符号秩检验，Wilcoxon significance, level of, 99 显著，水平simple hypothesis, 97 简单假设simulation, computer, to find null distribution, 446, 447 模拟，计算机, 求零假设分布size of the critical region, 100 临界域的大小slope, A.R.E. of rank test for, 335 斜率, A.R.E.秩检验slope in linear regression, 333 线性回归的斜率confidence interval for, 335 置信区间testing the, 335 检验Smirnov test, 456, Smirnov检验efficiency of, 465 效率exact tables, 558-560 精确表Smirnov-type tests for several samples, 462 多样本Smirnov型检验Spearman’s foottrule, 331 Spearman 脚规则Spearman’s rank correlation test, 175, 316 Spearman秩相关检验A.R.E. of, 327 A.R.E.exact tables, 544 精确表Spearman’s rho, 314, 325, 326, 335 Spearman’s rhofor ordered alternatives, 380 顺序备择relationship with Friedman’s test, 382 与Friedman检验的关系split plots, 385 裂区SPSS, v, 382, 390squared ranks test for variances, 300 方差的平方秩检验exact tables for, 542-543 精确表standard deviation, 37, 38 标准差estimation of, 443 估计of hypergeometric distribution, 188, 191 超几何分布population, estimator of, 115 总体，估计量sample, 83 样本standard error, 85, 88 标准差standard normal distribution, 55 标准正态分布STA TA, v, 88statistic, 75, 76 统计量order, 77, 82 次序test, 35,96, 97 检验STA TISTUICA, vstatistical inference, 68 统计推断statistics, 68 统计学StatMost, v, 259StatXact, v, 104, 127, 130, 144, 161, 168, 182, 189, 201, 205, 210, 220, 230, 241, 252, 276, 282, 290, 303, 318, 322, 325, 355, 361, 371, 375, 380, 382, 387, 399, 400, 401, 408, 409, 413, 432, 435, 444, 451, 459stem and leaf method, 270 茎叶方法step function, 52 阶梯函数stratified samples, 362 分层样本sum of chi-squared random variables, 62 χ2随机变量的和sum of integers formula, 40 整数和公式sum of random variables: 随机变量和mean of, 39 均值variance of, 48 方差sum of squared integers formula,43 整数平方和公式sure event, 14 必然事件survival curves, 119 生存曲线survival function, 89 生存函数empirical, 89 经验symmetric distributions, 350, 351 对称分布symmetry, Smirnov test for, 465 对称性，Smirnov检验symmetry, tests for, 364 对称性，检验SYSTA T, v, 88, 91, 259t distribution, table, 561 t分布，表格t statistic computed on ranks, 367 基于秩计算的t统计量t test: t检验,efficiency of paired, 364 配对效率one sample, 363, 418 一样本paired, 363 配对two sample, 284, 417 两样本table,contingency, 166, 179, 292 表，列联target population, 69, 70 目标总体tau, Kendall’s, 318, 319, 325, 326, 335 tau, Kendall test, conservative, 113 检验, 保守的test, hypothesis, 95 检验，假设test, one tailed, 98 检验，单边test, statistic, 3, 96, 97 检验，统计量test,unbiased, 106, 108, 160 检验，无偏testing hypotheses, 95 假设检验tests, consistent sequence of, 106, 108, 160 检验，相合序列three-way contingency table, 214 三种方式列联表tolerance limits, 150 容忍限approximation formulas for, 151, 155 逼近公式exact tables for, 537 精确表tansformation, rank, 417 变换，秩trend: 趋势Cox and Stuart test for, 169, 170 Cox和Stuart检验Daniel’s test for, 232 Daniel检验trials, 6 基本试验Tschuprow’s coefficient, 232 Tschuprow系数two independent samples, randomization test for, 409 两独立样本，随机化检验two-sample Cramér-von Mises test, 463 两样本Cramér-von Mises检验two-sample t test, 198 两样本t检验two-tailed test, 98 双边t检验two-way contingency table, 214 两种方式列联表typ eⅠerror , 98 一类错误typ eⅡerror, 98, 99 二类错误unbiased estimator, 84, 94 无偏估计量unbiased, sign test, 163 无偏，符号检验unbiased test, 106, 108, 160 无偏检验uniform distribution: 均匀分布continuous, 433 连续discrete, 28, 437 离散upper-tailed test, 98 右边检验value, expected,35, 39 值，期望van der Waerden test, 397 van der Waerden检验variable, random, 22, 23, 76 变量，随机variance, 36, 37 方差in binomial distribution, 49 二项分布multiple comparisons for test for, 304 检验的多重比较in rank test using scores, 307 得分秩检验sample, 81, 83 样本squared ranks test for, 300 平方秩检验of sum of random variables, 48 随机变量的和of sum of ranks, 48, 49 秩和tests for, 309 检验variations of the sign test, 166, 175 符号检验的变差Walsh test, 364 Walsh检验websites, Internet, v 网址，因特耐特网Wilcoxon signed ranks test, 164, 352, 411 Wilcoxon符号秩检验continuity correction in, 359 连续相关efficiency of, 364 效率extension to k samples of, 367 推广到k个样本normal approximation in, 353, 359 正态逼近tables, 547-548 表格Wilcoxon test, 103 Wilcoxon检验Wilcoxon two-sample test, 271 Wilcoxon两样本检验。

数据库课件

Copyright © 2000 The McGraw-Hill Companies. All Rights reserved
SYSTEMS ANALYSIS AND DESIGN METHODS 5th Edition
Whitten Bentley Dittman
Pros and Cons of Databases
SYSTEMS ANALYSIS AND DESIGN METHODS 5th Edition
Whitten Bentley Dittman
Files
A file is the set of all occurrences of a given record structure. A table is the relational database equivalent of a file.
Pros
• Ability to share data across applications • Less, and controlled redundancy (total nonredundancy is not achievable) • Data independence from applications increases adaptability • Superior scalability
A blocking factor is the number of logical records included in a single read or write operation (from the computer’s perspective).

Irwin/McGraw-Hill
Copyright © 2000 The McGraw-Hill Companies. All Rights reserved

《离散数学》双语教学第一章真值表,逻辑和证明

《离散数学》双语教学第一章真值表，逻辑和证明《离散数学》双语教学第一章真值表，逻辑和证明CHAPTER 1TRUTH TABLES, LOGIC, AND PROOFSGlossarystatement, proposition:命题 logical connective:命题联结词compound statement:复合命题 propositional variable:命题变元negation:否定(式)truth table:真值表conjunction:合取 disjunction:析取 propositional function:命题公式fallacy: 谬误syllogism:三段论universal quantification:全称量词化 existential quantification:存在量词化 hypothesis(premise): 假设～前提～前件 conditional statement, implication:条件式～蕴涵式 consequent, conclusion:结论～后件 converse:逆命题contrapositive:逆否命题biconditional, equivalence:双条件式～等价(逻辑)等价的 logically equivalent:contingency:可满足式tautology:永真式(重言式)contradiction, absurdity:永假(矛盾)式 logically follow:是…的逻辑结论 argument:论证axioms:公理第 1 页共 47 页 2010-12-27《离散数学》双语教学第一章真值表，逻辑和证明 postulate:公设rules of reference:推理规则modus ponens:肯定律 modus tollens:否定律reductio ad absurdum:归谬律proof by contradiction:反证法counterexample:反例 minterm:极小项disjunctive normal form:主析取范式maxterm:极大项conjunctive normal form:主合取范式第 2 页共 47 页 2010-12-27《离散数学》双语教学第一章真值表，逻辑和证明本章内容及教学要点:1.1 Statements and Connectives教学内容:statements(propositions)～compound statement～connectives:negation～conjunction～disjunction～truth tables 1.2 Conditional Statements教学内容:implications(conditional statements)～biconditional～equivalent～and quantifications1.3 Equivalent Statements教学内容:logical equivalence～converse～inverse～contrapositive～tautology～contradiction(absurdity)～contingency～properties of logical connectives1.4 Axiomatic Systems: Arguments and Proofs教学内容:rules of reference～augument～valid argument～hypotheses～premises～law of detachment(modus ponens)～syllogism～modus tollens～addition～proof by contradiction 1.5 Normal Forms教学内容:minterm～disjunctive normal form～maxterm～conjunctive normal form定理证明及例题解答第 3 页共 47 页 2010-12-27《离散数学》双语教学第一章真值表，逻辑和证明Logic, developed by Aristotle, has been used through the centuries in the development of many areas of learning including theology, philosophy, and mathematics. It is the foundation on which the whole structure of mathematics is built. Basically it is the science of reasoning, which may allow us to determine statements about mathematics whether are true or false based on a set of basic assumptions called axioms. Logic is also used in computer science to construct computer programs and to show that programs do what they are designed to do.逻辑学是研究人的思维形式的科学. 而数理逻辑是逻辑学的一个重要分支～是用数学形式化的方法研究思维规律的一门学科. 由于它使用了一套符号来简洁地表达出各种推理的逻辑关系～故它又称符号逻辑.数理逻辑用数学方法研究推理、利用符号体系研究推理过程中前提和结论之间的关系. 数理逻辑的主要内容:逻辑演算(L和L)、公理化集合论、模型论、S p构造主义与证明论. 数理逻辑在电子线路、机器证明、自动化系统、编译理论、算法设计方法方面有广泛的应用.The rules of logic specify the meaning of mathematicalstatements. Logic is the basis of all mathematical reasoning, and it has practical applications to the design of computing machines, to system specifications, to artificial intelligence(AI), to computer programming, to programming languages, and to other areas of computer science, as well as to many other fields of study.第 4 页共 47 页 2010-12-27《离散数学》双语教学第一章真值表，逻辑和证明1.1 Statements and Connectivess(命题和联结词)命题逻辑研究的对象是命题及命题之间的逻辑关系.Propositions are the basic building blocks of logic. Many mathematical statements are constructed by combining one or more propositions.定义1.1.1 A proposition is a statement or declarative sentence that is either true or false, but not both,命题是一个非真即假的陈述句,.因此不能判断真假的陈述句、疑问句、祈使句和感叹句都不是命题.,1, The true or false value assigned to a statement is called its truth value; (一个命题的真或假称为命题的真值. 真用T或1表示～假用F或0表示),2, 一个陈述句有真值与是否知道它的真假是两回事.例1.1.1 判断下列语句是不是命题,若是～给出命题的真值: (1) 陕西师大不是一座工厂.(2) 你喜欢唱歌吗,(3) 给我一块钱吧:(4) 我不是陕西师大的学生.(5) 我正在说谎.Logical connectives(命题联结词)数理逻辑的特点是并不关心具体某个命题的真假～而是将逻辑推理变成类似数学演算的形式化过程, 关心的是命题之间的关联性. 因此需要进行命题符号化.命题联结词的作用是为了将简单命题组合成复合命题.We will now introduce the logical connectives that are used to form new propositions from existing propositions. And once truth values have been assigned to simple propositions, we can progress to more complicated compound statements.A statement that contains no connectives is called a simple第 5 页共 47 页 2010-12-27《离散数学》双语教学第一章真值表，逻辑和证明statement. We will use p,q,r…to represent simple statements(简单命题就是简单陈述句～用字母p,q,r…(或带下标)表示),Sometimes, the letters p,q,r,s,…are used to denote propositional variables that can be replacedby statements(命题变元:可以用命题代替的变元).A statement that contains logical connectives(命题联结词) is called compound statements(复合命题). In general, a compound statement may have many component parts, each of which is itself a statement, represented by some propositional variable. The truth of a compound proposition is determined by the truth or falsity of the component parts.propositional constant(命题常元):T(1)或F(0)～或者表示一个确定的命题,propositional variable(命题变元):可用一个特定的命题取代。

ExplainingNormalQuantile-QuantilePlotsthrough...

Explaining Normal Quantile-Quantile Plots through Animation:The Water-Filling AnalogyRobert A.StineDepartment of StatisticsThe Wharton School of the University of PennsylvaniaPhiladelphia,PA19104-6340September9,2016AbstractA normal quantile-quantile(QQ)plot is an important diagnostic for checking the as-sumption of normality.Though useful,these plots confuse students in my introductory statistics classes.A water-ﬁlling analogy,however,intuitively conveys the underlying concept.This analogy characterizes a QQ plot as a parametric plot of the water levels in two graduallyﬁlling vases.Each vase takes its shape from a probability distribution or sample.If the vases share a common shape,then the water levels match throughout theﬁlling,and the QQ plot traces a diagonal line.An R package qqvases provides an interactive animation of this process and is suitable for classroom use.Key words:Education,diagnostic,simulation.1Figure1:Though hard to judge from the histogram,the normal QQ plot shows that the distribution of daily percentage changes in the value of Apple stock in2014-2015has thicker tails than a normal distribution.1IntroductionNormal QQ plots are an important visual diagnostic,but one that can be hard toexplain.Students quickly learn that if the data in a normal QQ plot deviate from adiagonal reference line,then the assumption of normality is questionable.For example,Figure1illustrates the diﬃculty of judging normality from a histogram.The data aredaily percentage changes in the value of Apple stock in2014-2015.The histogram isbell-shaped,but the distribution has thicker tails than anticipated by normality.Thedeviations from the diagonal line in the normal QQ plot imply that,in the extremes,the data extend farther out than expected under normality.While they recognize itsimportance,many of my students have treated this plot as a graphical“black box”:auseful diagnostic that relies on a magical mechanism.In the spirit of Brown and Kass(2009)and Cobb(2015),this paper oﬀers a heuristic that makes these“fundamentalconcepts accessible.”2Water-ﬁlling analogyA normal QQ plot compares the shape of the empirical distribution of a sample to theshape of a normal distribution.To set up the analogy,consider comparing the shapeof a continuous distribution to that of the normal.Quantile plots graph percentilesof the distributions and therein lies the diﬃculty for students.Many of my studentsFigure2:Diﬀerent water levels in two vases reﬂect the diﬀerent shapes of the underlying distributions.The pair in the left frame are10%full,then50%full in the middle frame,and ﬁnally80%full on the right.ﬁnd a cumulative distribution confusing enough without considering its inverse.A sim-ple analogy,however,makes quantile functions more ly,quantilefunctions are analogous to water levels as weﬁll transparent vases.Figure2illustrates the idea.The“vase”on the left of each frame of Figure2is formed by gluing a gamma density function with its mirror image.Similarly,the vaseon the right of each frame is a Gaussian vase.Both vases have the same“volume”(really,area).To limit the heights of the vases,both are truncated at the0.0005and0.9995percentiles.(I call these containers vases because of their resemblance to vaseplots(Benjamini,1988).)Now imagine simultaneouslyﬁlling the two vases at equalrates with water,as suggested by the sequence of plots in theﬁgure.The left frameshows the two vases,initially10%full.The middle frame shows themﬁlled to50%,and the right frame shows them80%full.If two vases have the same shape,then thewater levels match throughout theﬁlling.Otherwise,as in this example,oneﬁlls moreslowly than the other,and the levels diﬀer.The level in the gamma vase grows slowlyat the start of theﬁlling because it has a wide base.As theﬁlling proceeds,the levelin the gamma vase eventually catches up with the level in the Gaussian vase becauseboth vases hold the same amount.In this context,a normal QQ plot is the parametric plot of these water levels.The level of the Gaussian vase determines the coordinate on the x-axis,and the level ofthe other vase gives the coordinate for the y-axis.Figure3shows the normal quantileplot for the two vases in Figure2,as rendered by the accompanying application.Tomake the linkage between this graph and the vases explicit,theﬁgure displays halvesof the vases(the density functions)along the respective axes.The quantile plot addsFigure3:This view of the open-source application shows the normal QQ plot for a gamma distribution.Adjacent vases reinforce the water-ﬁlling analogy as the quantiles increase.a diagonal line to make it easier to identify curvature.Controls in the application shown in Figure3allow interactive modiﬁcations.The percentile slider controls the water level;for example,moving the slider to the rightincreases the water level and extends the curve in the plot.Other controls change thedistribution that deﬁnes the y-axis;choices include a normal distribution,the showngamma distribution(with shape parameter3),a beta distribution,t-distributions(with3and6degrees of freedom),and a mixture of a normal and gamma.3Empirical QQ plotsApplying this analogy to the normal QQ plot of data requires more work and imagina-tion for two reasons.First,it would not make sense toﬁll a“discrete vase”–the waterwould leak out.Second,normal QQ plots of data should include bands that indicatewhether deviations from the diagonal are large enough to imply a signiﬁcant departurefrom normality.To address theﬁrst problem,statistics oﬀers a variety of smooth density estimates, but these estimates are unfamiliar to students taking introductory statistics.For ex-ample,a kernel density provides a continuous density estimate,and these have beenused to enhance boxplots(Hintze and Nelson,1998).A kernel density estimate,how-ever,diverts attention from the QQ plot to itself.Rather than take that route,then,the accompanying software shows a histogram of data.(The statistics package JMPadopts a similar presentation.)Because observations in a tall histogram bin are rel-atively closely packed,the heights of the bins in the histogram inversely convey the average rate of water-ﬁlling within an interval.For the second problem,there are simple approximations that quantify the size of a departure from the reference line.Students recognize that there is a problem when they see deviations like those in Figure1,but the decision of whether a deviation is “large enough”(statistically signiﬁcant)is a tough call for a student who is new to QQ plots.Bands remove this subjectivity by indicating how much departure from the reference line can be produced by sampling variation.A student doesn’t have to guess whether the data drift far from the reference line;they can see whether points fall outside the bands.For setting the bounds in the normal quantile plot,a variety of elaborate methods are available.Aldor-Noiman,Brown,Buja,Rolke,and Stine(2013)review several powerful proposals,but the accompanying animation requires limits that can be com-puted quickly.With that in mind,bounds for the deviation from normalityﬁrst tabled in Lilliefors(1967)work nicely.These tables adjust for the use of estimated parameters in the normal distribution.The tables give the value cαsuch thatlim n P(supx|F n(x)− Φ(x)|≤cα/√n)≈1−α,(1)where F n denotes the empirical distribution of the data and Φdenotes the cumulative normal distribution with estimated parameters X and s2.The asymptotic critical valuefor sup x|F n(x)− Φ(x)|≈0.89/√n ifα=0.05.For example,Figure4shows an example of an normal QQ plot of a sample of200observations from a gamma density,ﬁlled to the75th percentile.Selecting the“Sampledistribution?”checkbox in the application dialog produces an empirical QQ plot.Ahistogram replaces the distribution on the y-axis.Points in this sample drift outsidethe limits,indicating a statistically signiﬁcant departure from normality.(These arehighlighted in red in theﬁgure.)4DiscussionI must admit that you do not need a computer animation to teach quantile plots thisway.The water-ﬁlling analogy alone seems to take the mystery out of QQ plots.IFigure4:This animation shows the normal QQ plot of a sample of200observations from a gamma distribution.sketch two vases side-by-side on a blackboard,say that each vase holds a liter,andgradually“ﬁll”the vases by coloring in the levels with chalk or a marker.Students arequick to recognize that the levels–the quantiles–remain equal only if the vases havethe same shape.In that case,a graph of the level of one vase versus the level of theother falls along a diagonal line.I then sketch a blackboard version of Figure2andask the students to tell me how the graph of the levels will look.This discussion is alsoa nice opportunity to convey what is meant by the shape of a distribution.For those who want to use software,the animation can be run either on-line or in-stalled locally.Those with less interest in R can run the application remotely by point-ing their browser to :3838/stine/qqvases/.Readers familiar with R can download the package qqvases from the CRAN repositoryor from links on my web page /∼stine/.The softwareexploits shiny,a library for R used here to render plots with interactive controls ina browser window(Chang,Cheng,Allaire,Xie,and McPherson,2015).Running thecommand qq vase plot locally allows the user to customize the application,such asadding more distributions and generating QQ plots of data.In addition to explaining QQ plots,the software can be used to illustrate other fundamental concepts,such as Type I errors(the quantile plot of a sample from anormal distribution has data outside the bands)and power(the bands in an QQ plotbecome tighter as the sample size grows).It can be surprising to see how hard it is torecognize that small samples from a gamma distribution diﬀer signiﬁcantly from thenormal.Some students do ask about the origin of the conﬁdence bands.I don’t have a simple analogy explaining those,so I use the question as an opportunity to advertise more advanced courses.It is not unusual to see quantile plots explained with the help of showing dis-tributions along the axes(e.g.,the cover and Figure3.4of Verzani,2005),but to my knowledge authors have not exploited the water-ﬁlling analogy and resulting animation. This analogy is used to explain normal quantile plots in a textbook citepstinefoster14, but Iﬁnd that it works better when animated.ReferencesAldor-Noiman,S.,Brown,L.D.,Buja,A.,Rolke,W.,and Stine,R.A.(2013),“The power to see:A new graphical test of normality,”The American Statistician,67, 249–260.Benjamini,Y.(1988),“Opening the box of a boxplot,”The American Statistician,42, 257–262.Brown,E.N.and Kass,R.E.(2009),“What is statistics?”The American Statistician, 63,105–110.Chang,W.,Cheng,J.,Allaire,J.,Xie,Y.,and McPherson,J.(2015),shiny:Web Application Framework for R,r package version0.11.1.Cobb,G.(2015),“Mere renovation is too little too late:We need to rethink our undergraduate curriculum from the ground up,”The American Statistician,69,266–281.Hintze,J.L.and Nelson,R.D.(1998),“Violin plots:A box plot-density trace syner-gism,”The American Statistician,52,181–184.Lilliefors,H.W.(1967),“On the Kolmogorov-Smirnov test for normality with mean and variance unknown,”Journal of the Amer.Statist.Assoc.,62,399–402.Verzani,J.(2005),Using R for Introductory Statistics,Boca Raton FL:Chapman& Hall/CRC.。

Statistical_tables

Statistical TablesTable A2 The standard Normal distributionz 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641 0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247 0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859 0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .18670.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .16111.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379 1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985 1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823 1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681 1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559 1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .02941.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .02332.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064 2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036 2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026 2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .00192.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .00143.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010Table A3 Percentage points of the t distributionThe table gives critical values of the t distribution cutting off an area α in each tail, shown bythe top row of the table.Area (α) in each tailv 0.4 0.25 0.1 0.05 0.025 0.01 0.005 0.0025 0.001 0.00051 0.325 1.000 3.078 6.314 12.706 31.821 63.657 127.320 318.310 636.6202 0.289 0.816 1.886 2.920 4.303 6.965 9.925 14.089 22.327 31.5983 0.277 0.765 1.638 2.353 3.182 4.541 5.841 7.453 10.214 12.9244 0.271 0.741 1.533 2.132 2.776 3.747 4.604 5.598 7.173 8.6105 0.267 0.727 1.476 2.015 2.571 3.365 4.032 4.773 5.893 6.8696 0.265 0.718 1.440 1.943 2.447 3.143 3.707 4.317 5.208 5.9597 0.263 0.711 1.415 1.895 2.365 2.998 3.499 4.029 4.785 5.4088 0.262 0.706 1.397 1.860 2.306 2.896 3.355 3.833 4.501 5.0419 0.261 0.703 1.383 1.833 2.262 2.821 3.250 3.690 4.297 4.78110 0.260 0.700 1.372 1.812 2.228 2.764 3.169 3.581 4.144 4.58711 0.260 0.697 1.363 1.796 2.201 2.718 3.106 3.497 4.025 4.43712 0.259 0.695 1.356 1.782 2.179 2.681 3.055 3.428 3.930 4.31813 0.259 0.694 1.350 1.771 2.160 2.650 3.012 3.372 3.852 4.22114 0.258 0.692 1.345 1.761 2.145 2.624 2.977 3.326 3.787 4.14015 0.258 0.691 1.341 1.753 2.131 2.602 2.947 3.286 3.733 4.07316 0.258 0.690 1.337 1.746 2.120 2.583 2.921 3.252 3.686 4.01517 0.257 0.689 1.333 1.740 2.110 2.567 2.898 3.222 3.646 3.96518 0.257 0.688 1.330 1.734 2.101 2.552 2.878 3.197 3.610 3.92219 0.257 0.688 1.328 1.729 2.093 2.539 2.861 3.174 3.579 3.88320 0.257 0.687 1.325 1.725 2.086 2.528 2.845 3.153 3.552 3.85021 0.257 0.686 1.323 1.721 2.080 2.518 2.831 3.135 3.527 3.81922 0.256 0.686 1.321 1.717 2.074 2.508 2.819 3.119 3.505 3.79223 0.256 0.685 1.319 1.714 2.069 2.500 2.807 3.104 3.485 3.76724 0.256 0.685 1.318 1.711 2.064 2.492 2.797 3.091 3.467 3.74525 0.256 0.684 1.316 1.708 2.060 2.485 2.787 3.078 3.450 3.72526 0.256 0.684 1.315 1.706 2.056 2.479 2.779 3.067 3.435 3.70727 0.256 0.684 1.314 1.703 2.052 2.473 2.771 3.057 3.421 3.69028 0.256 0.683 1.313 1.701 2.048 2.467 2.763 3.047 3.408 3.67429 0.256 0.683 1.311 1.699 2.045 2.462 2.756 3.038 3.396 3.65930 0.256 0.683 1.310 1.697 2.042 2.457 2.750 3.030 3.385 3.646 40 0.255 0.681 1.303 1.684 2.021 2.423 2.704 2.971 3.307 3.551 60 0.254 0.679 1.296 1.671 2.000 2.390 2.660 2.915 3.232 3.460 120 0.254 0.677 1.289 1.658 1.980 2.358 2.617 2.860 3.160 3.373 ∞0.253 0.674 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.291Table A4 Critical values of the χ2The values in the table give the critical values of χ distribution2Area in right-hand tailwhich cut off the area in the right-hand tail given at the top of the column.v0.9950.9900.9750.9500.9000.7500.5001 392704.10157088.10−10 982069.10−9 393214.10−9 0.0157908 −80.1015308 0.454936 2 0.0100251 0.0201007 0.0506356 0.102587 0.210721 0.575364 1.38629 3 0.0717218 0.114832 0.215795 0.351846 0.584374 1.212534 2.36597 4 0.206989 0.297109 0.484419 0.710723 1.063623 1.92256 3.35669 5 0.411742 0.554298 0.831212 1.145476 1.61031 2.67460 4.35146 6 0.675727 0.872090 1.23734 1.63538 2.20413 3.45460 5.34812 7 0.989256 1.239043 1.68987 2.16735 2.83311 4.25485 6.34581 8 1.34441 1.64650 2.17973 2.73264 3.48954 5.07064 7.34412 9 1.73493 2.08790 2.70039 3.32511 4.16816 5.89883 8.34283 10 2.15586 2.55821 3.24697 3.94030 4.86518 6.73720 9.34182 11 2.60322 3.05348 3.81575 4.57481 5.57778 7.58414 10.3410 12 3.07382 3.57057 4.40379 5.22603 6.30380 8.43842 11.3403 13 3.56503 4.10692 5.00875 5.89186 7.04150 9.29907 12.3398 14 4.07467 4.66043 5.62873 6.57063 7.78953 10.1653 13.3393 15 4.60092 5.22935 6.26214 7.26094 8.54676 11.0365 14.3389 16 5.14221 5.81221 6.90766 7.96165 9.31224 11.9122 15.3385 17 5.69722 6.40776 7.56419 8.67176 10.0852 12.7919 16.3382 18 6.26480 7.01491 8.23075 9.39046 10.8649 13.6753 17.3379 19 6.84397 7.63273 8.90652 10.1170 11.6509 14.5620 18.3377 20 7.43384 8.26040 9.59078 10.8508 12.4426 15.4518 19.3374 21 8.03365 8.89720 10.28293 11.5913 13.2396 16.3444 20.3372 22 8.64272 9.54249 10.9823 12.3380 14.0415 17.2396 21.3370 23 9.26043 10.19567 11.6886 13.0905 14.8480 18.1373 22.3369 249.8862310.8564 12.4012 13.8484 15.6587 19.0373 23.3367 25 10.5197 11.5240 13.1197 14.6114 16.4734 19.9393 24.3266 26 11.1602 12.1981 13.8439 15.3792 17.2919 20.8434 25.3365 27 11.8076 12.8785 14.5734 16.1514 18.1139 21.7494 26.3363 28 12.4613 13.5647 15.3079 16.9279 18.9392 22.6572 27.3362 29 13.1211 14.2565 16.0471 17.7084 19.7677 23.5666 28.3361 30 13.7867 14.9535 16.7908 18.4927 20.5992 24.4776 29.3360 40 20.7065 22.1643 24.4330 26.5093 29.0505 33.6603 39.3353 50 27.9907 29.7067 32.3574 34.7643 37.6886 42.9421 49.3349 60 35.5345 37.4849 40.4817 43.1880 46.4589 52.2938 59.3347 70 43.2752 45.4417 48.7576 51.7393 55.3289 61.6983 69.3345 80 51.1719 53.5401 57.1532 60.3915 64.2778 71.1445 79.3343 90 59.1963 61.7541 65.6466 69.1260 73.2911 80.6247 89.3342 100 67.327670.064974.221977.929582.358190.133299.3341v .250 0.100 0.050 0.025 0.010 0.005 0.0011 1.32330 2.70554 003.84146 5.02389 6.63490 7.87944 10.8282 2.77259 4.60517 5.99146 7.37776 9.21034 10.5966 13.8163 4.10834 6.25139 7.81473 9.34840 11.3449 12.8382 16.2664 5.38527 7.77944 9.48773 11.1433 13.2767 14.8603 18.4675 6.62568 9.23636 11.0705 12.8325 15.0863 16.7496 20.5156 7.84080 10.6446 12.5916 14.4494 16.8119 18.5476 22.4587 9.03715 12.0170 14.0671 16.0128 18.4753 20.2777 24.3228 10.2189 13.3616 15.5073 17.5345 20.0902 21.9550 26.1259 11.3888 14.6837 16.9190 19.0228 21.6660 23.5894 27.87710 12.5489 15.9872 18.3070 20.4832 23.2093 25.1882 29.58811 13.7007 17.2750 19.6751 21.9200 24.7250 26.7568 31.26412 14.8454 18.5493 21.0261 23.3367 26.2170 28.2995 32.90913 15.9839 19.8119 22.3620 24.7356 27.6882 29.8195 34.52814 17.1169 21.0641 23.6848 26.1189 29.1412 31.3194 36.12315 18.2451 22.3071 24.9958 27.4884 30.5779 32.8013 37.69716 19.3689 23.5418 26.2962 28.8454 31.9999 34.2672 29.25217 20.4887 24.7690 27.5871 30.1910 33.4087 35.7185 40.79018 21.6049 25.9894 28.8693 31.5264 34.8053 37.1565 42.31219 22.7178 27.2036 30.1435 32.8523 36.1909 38.5823 43.82020 23.8277 28.4120 31.4104 34.1696 37.5662 39.9968 45.31521 24.9348 29.6151 32.6706 35.4789 38.9322 41.4011 46.79722 26.40393 30.8133 33.9244 36.7807 40.2894 42.7957 48.26823 27.1413 32.0069 35.1725 38.0756 41.6384 44.1813 49.72824 28.2412 33.1962 36.4150 39.3641 42.9798 45.5585 51.17925 29.3389 34.3816 37.6525 40.6465 44.3141 46.9279 52.61826 30.4346 35.5632 38.8851 41.9232 45.6417 48.2899 54.05227 31.5284 36.7412 40.1133 43.1945 46.9629 49.6449 55.47628 32.6205 37.9150 41.3371 44.4608 48.2782 50.9934 56.89229 33.7109 39.0875 42.5570 45.7223 49.5879 52.3356 58.30130 34.7997 40.2560 43.7730 46.9792 50.8922 53.6720 59.703 40 45.6160 51.8051 55.7585 59.3417 63.6907 66.7660 73.402 50 56.3336 63.1671 67.5048 71.4202 76.1539 79.4900 86.661 60 66.9815 74.3970 79.0819 83.2977 88.3794 91.9517 99.607 70 77.5767 85.5270 90.5312 95.0232 100.425 104.215 112.317 80 88.1303 96.5782 101.879 106.629 112.329 116.321 124.839 90 98.6499 107.565 113.145 118.136 124.116 128.299 137.208 100 109.141 118.498 124.342 129.561 135.807 140.169 149.449Table A5(a) Critical values of the F distribution (upper 5% points)The entries in the table give the critical values of F cutting off 5% in the right-hand tail of thedistribution. v1 gives the degrees of freedom in the numerator, v2 v those in the denominator.11 2 3 4 5 6 7 8 9v21 161.45 199.50 215.71 224.58 230.16 230.99 236.77 238.88 240.542 18.513 19.000 19.164 19.247 19.296 19.330 19.353 19.371 19.3853 10.128 9.5521 9.2766 9.1172 9.0135 8.9406 8.8867 8.8452 8.81234 7.7086 6.9443 6.5914 6.3882 6.2561 6.1631 6.0942 6.0410 5.99885 6.6079 5.7861 5.4095 5.1922 5.0503 4.9503 4.8759 4.8183 4.77256 5.9874 5.1433 4.7571 4.5337 4.3874 4.2839 4.2067 4.1468 4.09907 5.5914 4.7374 4.3468 4.1203 3.9715 3.8660 3.7870 3.7257 3.67678 5.3177 4.4590 4.0662 3.8379 3.6875 3.5806 3.5005 3.4381 3.38819 5.1174 4.2565 3.8625 3.6331 3.4817 3.3738 3.2927 3.2296 3.178910 4.9646 4.1028 3.7083 3.4780 3.3258 3.2172 3.1355 3.0717 3.020411 4.8443 3.9823 3.5874 3.3567 3.2039 3.0946 3.0123 2.9480 2.896212 4.7472 3.8853 3.4903 3.2592 3.1059 2.9961 2.9134 2.8486 2.796413 4.6672 3.8056 3.4105 3.1791 3.0254 2.9153 2.8321 2.7669 2.714414 4.6001 3.7389 3.3439 3.1122 2.9582 2.8477 2.7642 2.6987 2.645815 4.5431 3.6823 3.2874 3.0556 2.9013 2.7905 2.7066 2.6408 2.587616 4.4940 3.6337 3.2389 3.0069 2.8524 2.7413 2.6572 2.5911 2.537717 4.4513 3.5915 3.1968 2.9647 2.8100 2.6987 2.6143 2.5480 2.494318 4.4139 3.5546 3.1599 2.9277 2.7729 2.6613 2.5767 2.5102 2.456319 4.3807 3.5219 3.1274 2.8951 2.7401 2.6283 2.5435 2.4768 2.422720 4.3512 3.4928 2.0984 2.8661 2.7109 2.5990 2.5140 2.4471 2.392821 4.3248 3.4668 3.0725 2.8401 2.6848 2.5727 2.4876 2.4205 2.366022 4.3009 3.4434 3.0491 2.8167 2.6613 2.5491 2.4638 2.3965 2.341923 4.2793 3.4221 3.0280 2.7955 2.6400 2.5277 2.4422 2.3748 2.320124 4.2597 3.4028 3.0088 2.7763 2.6307 2.5082 2.4226 2.3551 2.300225 4.2417 3.3852 2.9912 2.7587 2.6030 2.4904 2.4047 2.3371 2.282126 4.2252 3.3690 2.9752 2.7426 2.5868 2.4741 2.3883 2.3205 2.265527 4.2100 3.3541 2.9604 2.7278 2.5719 2.4591 2.3732 2.3053 2.250128 4.1960 3.3404 2.9467 2.7141 2.5581 2.4453 2.3593 2.2913 2.236029 4.1830 3.3277 2.9340 2.7014 2.5454 2.4324 2.3463 2.2783 2.222930 4.1709 3.3158 2.9223 2.6896 2.5336 2.4205 2.3343 2.2662 2.2107 40 4.0847 3.2317 2.8387 2.6060 2.4495 2.3359 2.2490 2.1802 2.1240 60 4.0012 3.1504 2.7581 2.5252 2.3683 2.2541 2.1665 2.0970 2.0401 120 3.9201 3.0718 2.6802 2.4472 2.2899 2.1750 2.0868 2.0164 1.9588 ∞ 3.8415 2.9957 2.6049 2.3719 2.2141 2.0986 2.0096 1.9384 1.8799v110 12 15 20 24 30 40 60 120 ∞v21 241.88 243.91 245.95 248.01 249.05 250.10 251.14 252.20 253.25 254.312 19.396 19.413 19.429 19.446 19.454 19.462 19.471 19.479 19.487 19.4963 8.7855 8.7446 8.7029 8.6602 8.6385 8.6166 8.5944 8.5720 8.5494 8.52644 5.9644 5.9117 5.8578 5.8025 5.7744 5.7459 5.7170 5.6877 5.6581 5.62815 4.7351 4.6777 4.6188 4.5581 4.5272 4.4957 4.4638 4.4314 4.3985 4.36506 4.0600 3.9999 3.9381 3.8742 3.8415 3.8082 3.7743 3.7398 3.7047 3.66897 3.6365 3.5747 3.5107 3.4445 3.4105 3.3758 3.3404 3.3043 3.2674 3.22988 3.3472 3.2839 3.2184 3.1503 3.1152 3.0794 3.0428 3.0053 2.9669 2.92769 3.1373 3.0729 3.0061 2.9365 2.9005 2.8637 2.8259 2.7872 2.7475 2.706710 2.9782 2.9130 2.8450 2.7740 2.7372 2.6996 2.6609 2.6211 2.5801 2.537911 2.8536 2.7876 2.7186 2.6464 2.6090 2.5705 2.5309 2.4901 2.4480 2.404512 2.7534 2.6866 2.6169 2.5436 2.5055 2.4663 2.4259 2.3842 2.3410 2.296213 2.6710 2.6037 2.5331 2.4589 2.4202 2.3803 2.3392 2.2966 2.2524 2.206414 2.6022 2.5342 2.4630 2.3879 2.3487 2.3082 2.2664 2.2229 2.1778 2.130715 2.5437 2.4753 2.4034 2.3275 2.2878 2.2468 2.2043 2.1601 2.1141 2.065816 2.4935 2.4247 2.3522 2.2756 2.2354 2.1938 2.1507 2.1058 2.0589 2.009617 2.4499 2.3807 2.3077 2.2304 2.1898 2.1477 2.1040 2.0584 2.0107 1.960418 2.4117 2.3421 2.2686 2.1906 2.1497 2.1071 2.0629 2.0166 1.9681 1.916819 2.3779 2.3080 2.2341 2.1555 2.1141 2.0712 2.0264 1.9795 1.9302 1.878020 2.3479 2.2776 2.2033 2.1242 2.0825 2.0391 1.9938 1.9464 1.8963 1.843221 2.3210 2.2504 2.1757 2.0960 2.0540 2.0102 1.9645 1.9165 1.8657 1.811722 2.2967 2.2258 2.1508 2.0707 2.0283 1.9842 1.9380 1.8894 1.8380 1.783123 2.2747 2.2036 2.1282 2.0476 2.0050 1.9605 1.9139 1.8648 1.8128 1.757024 2.2547 2.1834 2.1077 2.0267 1.9838 1.9390 1.8920 1.8424 1.7896 1.733025 2.2365 2.1649 2.0889 2.0075 1.9643 1.9192 1.8718 1.8217 1.7684 1.711026 2.2197 2.1479 2.0716 1.9898 1.9464 1.9010 1.8533 1.8027 1.7488 1.690627 2.2043 2.1323 2.0558 1.9736 1.9299 1.8842 1.8361 1.7851 1.7306 1.671728 2.1900 2.1179 2.0411 1.9586 1.9147 1.8687 1.8203 1.7689 1.7138 1.654129 2.1768 2.1045 2.0275 1.9446 1.9005 1.8543 1.8055 1.7537 1.6981 1.637630 2.1646 2.0921 2.0148 1.9317 1.8874 1.8409 1.7918 1.7396 1.6835 1.6223 40 2.0772 2.0035 1.9245 1.8389 1.7929 1.7444 1.6928 1.6373 1.5766 1.5089 60 1.9926 1.9174 1.8364 1.7480 1.7001 1.6491 1.5943 1.5343 1.4673 1.3893 120 1.9105 1.8337 1.7505 1.6587 1.6084 1.5543 1.4952 1.4290 1.3519 1.2539 ∞ 1.8307 1.7522 1.6664 1.5705 1.5173 1.4591 1.3940 1.3180 1.2214 1.0000Table A5(b) Critical values of the F distribution (upper 2.5% points)The entries in the table give the critical values of F cutting off 2.5% in the right-hand tail of thedistribution. v1 gives the degrees of freedom in the numerator, v2 v in the denominator.11 2 3 4 5 6 7 8 9v21 647.79 799.50 864.16 899.58 921.85 937.11 948.22 956.66 963.282 38.506 39.000 39.165 39.248 39.298 39.331 39.355 39.373 39.3873 17.443 16.044 15.439 15.101 14.885 14.735 14.624 14.540 14.4734 12.218 10.649 9.9792 9.6045 9.3645 9.1973 9.0741 8.9796 8.90475 10.007 8.4336 7.7636 7.3879 7.1464 6.9777 6.8531 6.7572 6.68116 8.8131 7.2599 6.5988 6.2272 5.9876 5.8198 5.6955 5.5996 5.52347 8.0727 6.5415 5.8898 5.5226 5.2852 5.1186 4.9949 4.8993 4.82328 7.5709 6.0595 5.4160 5.0526 4.8173 4.6517 4.5286 4.4333 4.35729 7.2093 5.7147 5.0781 4.7181 4.4844 4.3197 4.1970 4.1020 4.026010 6.9367 5.4564 4.8256 4.4683 4.2361 4.0721 3.9498 3.8549 3.779011 6.7241 5.2559 4.6300 4.2751 4.0440 3.8807 3.7586 3.6638 3.587912 6.5538 5.0959 4.4742 4.1212 3.8911 3.7283 3.6065 3.5118 3.435813 6.4143 4.9653 4.3472 3.9959 3.7667 3.6043 3.4827 3.3880 3.312014 6.2979 4.8567 4.2417 3.8919 3.6634 3.5014 3.3799 3.2853 3.209315 6.1995 4.7650 4.1528 3.8043 3.5764 3.4147 3.2934 3.1987 3.122716 6.1151 4.6867 4.0768 3.7294 3.5021 3.3406 3.2194 3.1248 3.048817 6.0420 4.6189 4.0112 3.6648 3.4379 3.2767 3.1556 3.0610 2.984918 5.9781 4.5597 3.9539 3.6083 3.3820 3.2209 3.0999 3.0053 2.921919 5.9216 4.5075 3.9034 3.5587 3.3327 3.1718 3.0509 2.9563 2.880120 5.8715 4.4613 3.8587 3.5147 3.2891 3.1283 3.0074 2.9128 2.836521 5.8266 4.4199 3.8188 3.4754 3.2501 3.0895 2.9686 2.8740 2.797722 5.7863 4.3828 3.7829 3.4401 3.2151 3.0546 2.9338 2.8392 2.762823 5.7498 4.3492 3.7505 3.4083 3.1835 3.0232 2.9023 2.8077 2.731324 5.7166 4.3187 3.7211 3.3794 3.1548 2.9946 2.8738 2.7791 2.702725 5.6864 4.2909 3.6943 3.3530 3.1287 2.9685 2.8478 2.7531 2.676626 5.6586 4.2655 3.6697 3.3289 3.1048 2.9447 2.8240 2.7293 2.652827 5.6331 4.2421 3.6472 3.3067 3.0828 2.9228 2.8021 2.7074 2.630928 5.6096 4.2205 3.6264 3.2863 3.0626 2.9027 2.7820 2.6872 2.610629 5.5878 4.2006 3.6072 3.2674 3.0438 2.8840 2.7633 2.6686 2.591930 5.5675 4.1821 3.5894 3.2499 3.0265 2.8667 2.7460 2.6513 2.5746 40 5.4239 4.0510 3.4633 3.1261 2.9037 2.7444 2.6238 2.5289 2.4519 60 5.2856 3.9253 3.3425 3.0077 2.7863 2.6274 2.5068 2.4117 2.3344 120 5.1523 3.8046 3.2269 2.8943 2.6740 2.5154 2.3948 2.2994 2.2217 ∞ 5.0239 3.6889 3.1161 2.7858 2.5665 2.4082 2.2875 2.1918 2.1136v110 12 15 20 24 30 40 60 120 ∞v21 968.63 976.71 984.87 993.10 997.25 1001.4 1005.6 1009.8 1014.0 1018.32 39.398 39.415 39.431 39.448 39.456 39.465 39.473 39.481 39.400 39.4983 14.419 14.337 14.253 14.167 14.124 14.081 14.037 13.992 13.947 13.9024 8.8439 8.7512 8.6565 8.5599 8.5109 8.4613 8.4111 8.3604 8.3092 8.25735 6.6192 6.5245 6.4277 6.3286 6.2780 6.2269 6.1750 6.1225 6.069? 6.01536 5.4613 5.3662 5.2687 5.1684 5.1172 5.0652 5.0125 4.9589 4.9044 4.84917 4.7611 4.6658 4.5678 4.4667 4.4150 4.3624 4.3089 4.2544 4.1989 4.14238 4.2951 4.1997 4.1012 3.9995 3.9472 3.8940 3.8398 3.7844 3.7279 3.67029 3.9639 3.8682 3.7694 3.6669 3.6142 3.5604 3.5055 3.4493 3.3918 3.332910 3.7168 3.6209 3.5217 3.4185 3.3654 3.3110 3.2554 3.1984 3.1399 3.079811 3.5257 3.4296 3.3299 3.2261 3.1725 3.1176 3.0613 3.0035 2.9441 2.882812 3.3736 3.2773 3.1772 3.0728 3.0187 2.9633 2.9063 2.8478 2.7874 2.724913 3.2497 3.1532 3.0527 2.9477 2.8932 2.8372 2.7797 2.7204 2.6590 2.595514 3.1469 3.0502 2.9493 2.8437 2.7888 2.7324 2.6742 2.6142 2.5519 2.487215 3.0602 2.9633 2.8621 2.7559 2.7006 2.6437 2.5850 2.5242 2.4611 2.395316 2.9862 2.8890 2.7875 2.6808 2.6252 2.5678 2.5085 2.4471 2.3831 2.316317 2.9222 2.8249 2.7230 2.6158 2.5598 2.5020 2.4422 2.3801 2.3153 2.247418 2.8664 2.7689 2.6667 2.5590 2.5027 2.4445 2.3842 2.3214 2.2558 2.186919 2.8172 2.7196 2.6171 2.5089 2.4523 2.3937 2.3329 2.2696 2.2032 2.133320 2.7737 2.6758 2.5731 2.4645 2.4076 2.3486 2.2873 2.2234 2.1562 2.085321 2.7348 2.6368 2.5338 2.4247 2.3675 2.3082 2.2465 2.1819 2.1141 2.042222 2.6998 2.6017 2.4984 2.3890 2.3315 2.2718 2.2097 2.1446 2.0760 2.003223 2.6682 2.5699 2.4665 2.3567 2.2989 2.2389 2.1763 2.1107 2.0415 1.967724 2.6396 2.5411 2.4374 2.3273 2.2693 2.2090 2.1460 2.0799 2.0099 1.935325 2.6135 2.5149 2.4110 2.3005 2.2422 2.1816 2.1183 2.0516 1.9811 1.905526 2.5896 2.4908 2.3867 2.2759 2.2174 2.1565 2.0928 2.0257 1.9545 1.878127 2.5676 2.4688 2.3644 2.2533 2.1946 2.1334 2.0693 2.0018 1.9299 1.852728 2.5473 2.4484 2.3438 2.2324 2.1735 2.1121 2.0477 1.9797 1.9072 1.829129 2.5286 2.4295 2.3248 2.2131 2.1540 2.0923 2.0276 1.9591 1.8861 1.807230 2.5112 2.4120 2.3072 2.1952 2.1359 2.0739 2.0089 1.9400 1.8664 1.7867 40 2.3882 2.2882 2.1819 2.0677 2.0069 1.9429 1.8752 1.8028 1.7242 1.6371 60 2.2702 2.1692 2.0613 1.9445 1.8817 1.8152 1.7440 1.6668 1.5810 1.4821 120 2.1570 2.0548 1.9450 1.8249 1.7597 1.6899 1.6141 1.5299 1.4327 1.3104 ∞ 2.0483 1.9447 1.8326 1.7085 1.6402 1.5660 1.4835 1.3883 1.2684 1.0000Table A5(c) Critical values of the F distribution (upper 1% points)The entries in the table give the critical values of F cutting off 1% in the right-hand tail of thedistribution. v1 gives the degrees of freedom in the numerator, v2 v in the denominator.11 2 3 4 5 6 7 8 9 v11 4052.2 4999.5 5403.4 5624.6 5763.6 5859.0 5928.4 5981.1 6022.52 98.503 99.000 99.166 99.249 99.299 99.333 99.356 99.374 99.3883 34.116 30.817 29.457 28.710 28.237 27.911 27.672 27.489 27.3454 21.198 18.000 16.694 15.977 15.522 15.207 14.976 14.799 14.6595 16.258 13.274 12.060 11.392 10.967 10.672 10.456 10.289 10.1586 13.745 10.925 9.7795 9.1483 8.7459 8.4661 8.2600 8.1017 7.97617 12.246 9.5466 8.4513 7.8466 7.4604 7.1914 6.9928 6.8400 6.71888 11.259 8.6491 7.5910 7.0061 6.6318 6.3707 6.1776 6.0289 5.91069 10.561 8.0215 6.9919 6.4221 6.0569 5.8018 5.6129 5.4671 5.351110 10.044 7.5594 6.5523 5.9943 5.6363 5.3858 5.2001 5.0567 4.942411 9.6460 7.2057 6.2167 5.6683 5.3160 5.0692 4.8861 4.7445 4.631512 9.3302 6.9266 5.9525 5.4120 5.0643 4.8206 4.6395 4.4994 4.387513 9.0738 6.7010 5.7394 5.2053 4.8616 4.6204 4.4410 4.3021 4.191114 8.8618 6.5149 5.5639 5.0354 4.6950 4.4558 4.2779 4.1399 4.029715 8.6831 6.3589 5.4170 4.8932 4.5556 4.3183 4.1415 4.0045 3.894816 8.5310 6.2262 5.2922 4.7726 4.4374 4.2016 4.0259 3.8896 3.780417 8.3997 6.1121 5.1850 4.6690 4.3359 4.1015 3.9267 3.7910 3.682218 8.2854 6.0129 5.0919 4.5790 4.2479 4.0146 3.8406 3.7054 3.597119 8.1849 5.9259 5.0103 4.5003 4.1708 3.9386 3.7653 3.6305 3.522520 8.0960 5.8489 4.9382 4.4307 4.1027 3.8714 3.6987 3.5644 3.456721 8.0166 5.7804 4.8740 4.3688 4.0421 3.8117 3.6396 3.5056 3.398122 7.9454 5.7190 4.8166 4.3134 3.9880 3.7583 3.5867 3.4530 3.345823 7.8811 5.6637 4.7649 4.2636 3.9392 3.7102 3.5390 3.4057 3.298624 7.8229 5.6136 4.7181 4.2184 3.8951 3.6667 3.4959 3.3629 3.256025 7.7698 5.5680 4.6755 4.1774 3.8550 3.6272 3.4568 3.3439 3.217226 7.7213 5.5263 4.6366 4.1400 3.8183 3.5911 3.4210 3.2884 3.181827 7.6767 5.4881 4.6009 4.1056 3.7848 3.5580 3.3882 3.2558 3.149428 7.6356 5.4529 4.5681 4.0740 3.7539 3.5276 3.3581 3.2259 3.119529 7.5977 5.4204 4.5378 4.0449 3.7254 3.4995 3.3303 3.1982 3.092030 7.5625 5.3903 4.5097 4.0179 3.6990 3.4735 3.3045 3.1726 3.0665 40 7.3141 5.1785 4.3126 3.8283 3.5138 3.2910 3.1238 2.9930 2.8876 60 7.0771 4.9774 4.1259 3.6490 3.3389 3.1187 2.9530 2.8233 2.7185 120 6.8509 4.7865 3.9491 3.4795 3.1735 2.9559 2.7918 2.6629 2.5586 ∞ 6.6349 4.6052 3.7816 3.3192 3.0173 2.8020 2.6393 2.5113 2.4073v110 12 15 20 24 30 40 60 120 ∞v21 6055.8 6106.3 6157.3 6208.7 6234.6 6260.6 6286.8 6313.0 6339.4 6365.92 99.399 99.416 99.433 99.449 99.458 99.466 99.474 99.482 99.491 99.4993 27.229 27.052 26.872 26.690 26.598 26.505 26.411 26.316 26.221 26.1254 14.546 14.374 14.198 14.020 13.929 13.838 13.745 13.652 13.558 13.4635 10.051 9.8883 9.7222 9.5526 9.4665 9.3793 9.2912 9.2020 9.1118 9.02046 7.8741 7.7183 7.5590 7.3958 7.3127 7.2285 7.1432 7.0567 6.9690 6.88007 6.6201 6.4691 6.3143 6.1554 6.0743 5.9920 5.9084 5.8236 5.7373 5.64958 5.8143 5.6667 5.5151 5.3591 5.2793 5.1981 5.1156 5.0316 4.9461 4.85889 5.2565 5.1114 4.9621 4.8080 4.7290 4.6486 4.5666 4.4831 4.3978 4.310510 4.8491 4.7059 4.5581 4.4054 4.3269 4.2469 4.1653 4.0819 3.9965 3.909011 4.5393 4.3974 4.2509 4.0990 4.0209 3.9411 3.8596 3.7761 3.6904 3.602412 4.2961 4.1553 4.0096 3.8584 3.7805 3.7008 3.6192 3.5355 3.4494 3.360813 4.1003 3.9603 3.8154 3.6646 3.5868 3.5070 3.4253 3.3413 3.2548 3.165414 3.9394 3.8001 3.6557 3.5052 3.4274 3.3476 3.2656 3.1813 3.0942 3.004015 3.8049 3.6662 3.5222 3.3719 3.2940 3.2141 3.1319 3.0471 2.9595 2.868416 3.6909 3.5527 3.4089 3.2587 3.1808 3.1007 3.0182 2.9330 2.8447 2.752817 3.5931 3.4552 3.3117 3.1615 3.0835 2.0032 2.9205 2.8348 2.7459 2.653018 3.5082 3.3706 3.2273 3.0771 2.9990 2.9185 2.8354 2.7493 2.6597 2.566019 3.4338 3.2965 3.1533 3.0031 2.9249 2.8442 2.7608 2.6742 2.5839 2.489320 3.3682 3.2311 3.0880 2.9377 2.8594 2.7785 2.6947 2.6077 2.5168 2.421221 3.3098 3.1730 3.0300 2.8796 2.8010 2.7200 2.6359 2.5484 2.4568 2.360322 3.2576 3.1209 2.9779 2.8274 2.7488 2.6675 2.5831 2.4951 2.4029 2.305523 3.2106 3.0740 2.9311 2.7805 2.7017 2.6202 2.5355 2.4471 2.3542 2.255824 3.1681 3.0316 2.8887 2.7380 2.6591 2.5773 2.4923 2.4035 2.3100 2.210725 3.1294 2.9931 2.8502 2.6993 2.6203 2.5383 2.4530 2.3637 2.2696 2.169426 3.0941 2.9578 2.8150 2.6640 2.5848 2.5026 2.4170 2.3273 2.2325 2.131527 3.0618 2.9256 2.7827 2.6316 2.5522 2.4699 2.3840 2.2938 2.1985 2.096528 3.0320 2.8959 2.7530 2.6017 2.5223 2.4397 2.3535 2.2629 2.1670 2.064229 3.0045 2.8685 2.7256 2.5742 2.4946 2.4118 2.3253 2.2344 2.1379 2.034230 2.9791 2.8431 2.7002 2.5487 2.4689 2.3860 2.2992 2.2079 2.1108 2.0062 40 2.8005 2.6648 2.5216 2.3689 2.2880 2.2034 2.1142 2.0194 1.9172 1.8047 60 2.6318 2.4961 2.3523 2.1978 2.1154 2.0285 1.9360 1.8363 1.7263 1.6006 120 2.4721 2.3363 2.1915 2.0346 1.9500 1.8600 1.7628 1.6557 1.5330 1.3805 ∞ 2.3209 2.1847 2.0385 1.8783 1.7908 1.6964 1.5923 1.4730 1.3246 1.0000Table A6 Critical values of Spearman’s rank correlation coefficientEntries in the table show critical values of Spearman’s rank correlation coefficient. The value at the top of each column shows the significance level for a two-tail test. For a one-tail test, the significance level is half that shown.N 10% 5% 2% 1%5 0.900 – – –6 0.829 0.886 0.943 –7 0.714 0.786 0.893 –8 0.643 0.738 0.833 0.8819 0.600 0.683 0.783 0.83310 0.564 0.648 0.745 0.81811 0.523 0.623 0.763 0.79412 0.497 0.591 0.703 0.78013 0.475 0.566 0.673 0.74614 0.457 0.545 0.646 0.71615 0.441 0.525 0.623 0.68916 0.425 0.507 0.601 0.66617 0.412 0.490 0.582 0.64518 0.399 0.476 0.564 0.62519 0.388 0.462 0.549 0.60820 0.377 0.450 0.534 0.59121 0.368 0.438 0.521 0.57622 0.359 0.428 0.508 0.56223 0.351 0.418 0.496 0.54924 0.343 0.409 0.485 0.53725 0.336 0.400 0.475 0.52626 0.329 0.392 0.465 0.51527 0.323 0.385 0.456 0.50528 0.317 0.377 0.448 0.49629 0.311 0.370 0.440 0.48730 0.305 0.364 0.432 0.47811。

Airbus320飞行设置手册

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8
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A320 V-SPEED ADJUSTMENTS
Minimum V1 / Vr / V2
CRUISE CHARTS
A320 Enroute Weight Limitations - Engine Inoperative
All flights must plan a route and/or limit the MTOGW so that the airplane will have sufficient performance to clear enroute terrain if an engine fails. Other airplanes can either dump fuel to reduce weight or they have sufficient engine inoperative performance so that MTOGW is not restricted. Since the A320 is unable to dump fuel, MTOGW may be limited on routes over mountainous terrain.
EPR NAM/1000 LBS Adjustments: • TAS (knots) is for standard temperature; add 1 knot/°C above standard, subtract 1 knot/°C below standard • Fuel consumption (1000 pounds/hour) = TAS for actual temperature + NAM/1000 pounds
Reduced EPR is the minimum thrust required under normal conditions and is recommended since it results in reduced engine wear and fuel consumption. Do not use reduced takeoff thrust when: • Braking action is reported less than good • The probability of windshear exists • Takeoff runway is other than dry • Headwind adjustment has been used to increase the allowable takeoff weight • Takeoff is made with a tailwind • EPR indications are inop • A brake is deactivated The FMGS automatically computes reduced takeoff thrust when a FLEX temp higher than ambient temp is entered on the MCDU TAKEOFF page. To determine FLEX (ASMD) temp, see the Takeoff Data provided by dispatch.

Parametric and Non-Parametric

Байду номын сангаас
8 10 z 1 2 8 10 z 1 2
xx z s
• On the tables for z =1 we get 0.3413. Then z = = 0.6826. This means that the probability of X assuming a value between 8 and 12 or P (8 < X < 12) IS 68.26%
Distributions
Normal Probability Distribution
• Characteristics of the normal probability distribution:
• Bell-shaped, single peak at the centre of the distribution. • The arithmetic mean, median and mode are equal and located in the centre of the distribution. Thus half the area under the normal curve is to the right of this centre point and the other half to the left of it. • It is symmetrical about the mean. • The distribution is asymptotic. The curve gets closer and closer to the X-axis but never actually touches it.
– subtract the mean of the data set from each observation – Divide each by the standard deviation

建模软件lingo使用教程

§1
LINGO 快速入门
当你在 windows 下开始运行 LINGO 系统时，会得到类似下面的一个窗口：
外层是主框架窗口，包含了所有菜单命令和工具条，其它所有的窗口将被包含在主窗口之下。在主窗口内的标题为 LINGO Model – LINGO1 的窗口是 LINGO 的默认模型窗口，建立的模型都都要在该窗口内编码实现。下面举两个例子。例 1.1 如何在 LINGO 中求解如下的 LP 问题：
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LINGO 教程
setname/member1..memberN/[: attribute_list]; 这里的 member1 是集的第一个成员名，memberN 是集的最末一个成员名。LINGO 将自动产生中间的所有成员名。 LINGO 也接受一些特定的首成员名和末成员名，用于创建一些特殊的集。列表如下：隐式成员列表格式 1..n StringM..StringN DayM..DayN MonthM..MonthN MonthYearM..MonthYearN 1..5 Car2..car14 Mon..Fri Oct..Jan Oct2001..Jan2002 示例 1,2,3,4,5 Car2,Car3,Car4,„,Car14 Mon,Tue,Wed,Thu,Fri Oct,Nov,Dec,Jan Oct2001,Nov2001,Dec2001,Jan2002 所产生集成员
注意：该命名规则同样适用于集成员名和属性名等的命名。
Member_list 是集成员列表。如果集成员放在集定义中，那么对它们可采取显式罗列和隐式罗列两种方式。如果集成员不放在集定义中，那么可以在随后的数据部分定义它们。 ① 当显式罗列成员时，必须为每个成员输入一个不同的名字，中间用空格或逗号搁开，允许混合使用。例 2.1 可以定义一个名为 students 的原始集，它具有成员 John、Jill、Rose 和 Mike，属性有 sex 和 age： sets: students/John Jill, Rose Mike/: sex, age; endsets ② 当隐式罗列成员时，不必罗列出每个集成员。可采用如下语法：

组合优化

Slack or Surplus表示接近等于的程度。

在约束条件是<=中，通常叫做松弛变量，在约束条件是>=中，通常叫过剩变量。

如果约束条件是=，则Slack or Surplus为0，该约束是个紧约束(或有效约束)。

如果一个约束条件错误，作为一个不可行解，Slack or Surplus为负数。

Slack or Surplus表示的是：约束离相等还差多少。

如果一个约束是矛盾的（模型无可行解），则Slack or surplus的值是负数。

知道这些，可以帮助我们发现在一个不可实行的模型（指没有存在同时满足所有约束条件的变量集合）中的错误的约束条件。

第2和第4行松弛变量均为0,说明对于最优解来讲,两个约束(第2和4行)均取等号,即都是紧约束.Dual Price (Shadow price)给出对偶价格的值。

表示每增加一个单位(约束右边的常数)，目标值改变的数量（在最大化问题中目标函数值是增加，在最小化问题中目标函数值是减少）。

比如，在上一个Min模型中第四行的1，表示2*x1 + x2 <= 600增加一个单位到2*x1 + x2 <= 601，可以使目标值增加-1(因为第一行是目标函数的Dual Price是-1)，即Objective value = 799;增加-1个单位到599会使目标值增加到801。

Lingo solution report中各项的含义（一）优化模型的组成优化模型包括以下3部分：l Objective Function：目标函数是一个能准确表达所要优化问题的公式。

l Variables：Decision variables（决策变量），在模型中所使用的变量。

l Constraints：约束条件。

（二）Lingo软件使用的注意事项（1）LINGO中不区分大小写字母，变量（和行名）可以使用不超过32个字符表示，且必须以字母开头。

（2）在命令方式下（Command Window中），必须先输入MODEL：表示开始输入模型。

DB2系统内置——SYSCAT.TABLES所有的字段说明

DB2系统内置——SYSCAT.TABLES所有的字段说明SYSCAT.TABLES catalog viewEach row represents a table, view, alias, or nickname. Each table or view hierarchy has one additional row representing the hierarchy table or hierarchy view that implements the hierarchy. Catalog tables and views are included.每⼀⾏代表⼀张表，视图，别名或昵称。

每个表或视图层次结构都有⼀个额外的⾏，代表实现层次结构的层次结构表或层次结构视图。

包括⽬录表和视图。

Table 67. SYSCAT.TABLES Catalog ViewColumn Name Data Type Nullable DescriptionTABSCHEMA VARCHAR(128)Schema name of the object.TABNAME VARCHAR(128)Unqualified name of the object.OWNER VARCHAR(128)Authorization ID under which the table, view, alias, or nickname was created.TYPE CHAR(1)Type of object.A = AliasG = Global temporary tableH = Hierarchy tableL = Detached tableN = NicknameS = Materialized query tableT = Table (untyped)U = Typed tableV = View (untyped)W = Typed viewSTATUS CHAR(1)Status of the object.C = Set integrity pendingN = NormalX = InoperativeBASE_TABSCHEMA VARCHAR(128)Y If TYPE = 'A', contains the schema name of the table, view, alias, or nickname that is referenced by this alias; null value otherwise.BASE_TABNAME VARCHAR(128)Y If TYPE = 'A', contains the unqualified name of the table, view, alias, or nickname that is referenced by this alias; null value otherwise.ROWTYPESCHEMA VARCHAR(128)Y Schema name of the row type for this table, if applicable; null value otherwise.ROWTYPENAME VARCHAR(128)Y Unqualified name of the row type for this table, if applicable; null value otherwise.CREATE_TIME TIMESTAMP Time at which the object was created. INVALIDATE_TIME TIMESTAMP Time at which the object was last invalidated.STATS_TIME TIMESTAMP Y Time at which any change was last made to recorded statistics for this object. Null if statistics are not collected.COLCOUNT SMALLINT Number of columns, including inherited columns (if any).TABLEID SMALLINT Internal logical object identifier.TBSPACEID SMALLINT Internal logical identifier for the primary table space for this object.CARD BIGINT Total number of rows; -1 if statistics are not collected.NPAGES BIGINT Total number of pages on which the rows of the table exist; -1 for a view or alias, or if statistics are not collected; -2 for a subtable or hierarchy table.FPAGES BIGINT Total number of pages; -1 for a view or alias, or if statistics are not collected; -2 for a subtable or hierarchy table.OVERFLOW BIGINT Total number of overflow records in the table; -1 for a view or alias, or if statistics are not collected; -2 for a subtable or hierarchy table.TBSPACE VARCHAR(128)Y Name of the primary table space for the table. If no other table space is specified, all parts of the table are stored in this table space. Null for aliases, views, and partitioned tables.partitioned tables.INDEX_TBSPACE VARCHAR(128)Y Name of the table space that holds all indexes created on this table. Null for aliases, views, and partitioned tables, or if the INDEX IN clause was omitted or specified with the same value as the IN clause of the CREATE TABLE statement.LONG_TBSPACE VARCHAR(128)Y Name of the table space that holds all long data (LONG or LOB column types) for this table. Null for aliases, views, and partitioned tables, or if the LONG IN clause was omitted or specified with the same value as the IN clause of the CREATE TABLE statement.PARENTS SMALLINT Y Number of parent tables for this object; that is, the number of referential constraints in which this object is a dependent.CHILDREN SMALLINT Y Number of dependent tables for this object; that is, the number of referential constraints in which this object is a parent.SELFREFS SMALLINT Y Number of self-referencing referential constraints for this object; that is, the number of referential constraints in which this object is both a parent and a dependent.KEYCOLUMNS SMALLINT Y Number of columns in the primary key.KEYINDEXID SMALLINT Y Index identifier for the primary key index; 0 or the null value if there is no primary key.KEYUNIQUE SMALLINT Number of unique key constraints (other than the primary key constraint) defined on this object.CHECKCOUNT SMALLINT Number of check constraints defined on this object.DATACAPTURE CHAR(1)L = Table participates in data replication, including replication of LONG VARCHAR and LONG VARGRAPHIC columnsN = Table does not participate in data replication Y = Table participates in data replication, excluding replication of LONG VARCHAR and LONG VARGRAPHIC columnsCONST_CHECKED CHAR(32)Byte 1 represents foreign key constraint.Byte 2 represents check constraint.Byte 5 represents materialized query table.Byte 6 represents generated column.Byte 7 represents staging table.Byte 8 represents data partitioning constraint.Other bytes are reserved for future use. Possible values are:F = In byte 5, the materialized query table cannotbe refreshed incrementally. In byte 7, the contentof the staging table is incomplete and cannot beused for incremental refresh of the associatedmaterialized query table.N = Not checkedU = Checked by userW = Was in 'U' state when the table was placedin set integrity pending stateY = Checked by systemPMAP_ID SMALLINT Y Identifier for the distribution map that is currently in use by this table (null for aliases or views).PARTITION_MODE CHAR(1)Indicates how data is distributed among database partitions in a partitioned database system.H = HashingR = Replicated across database partitionsBlank = No database partitioningLOG_ATTRIBUTE CHAR(1)Always 0. This column is no longer used.PCTFREE SMALLINT Percentage of each page to be reserved for future inserts.Column Name Data Type Nullable Descriptioninserts.APPEND_MODE CHAR(1)Controls how rows are inserted into pages.N = New rows are inserted into existing spaces, ifavailableY = New rows are appended to the end of thedataInitial value is 'N'.REFRESH CHAR(1)Refresh mode.D = DeferredI = ImmediateO = OnceBlank = Not a materialized query tableREFRESH_TIME TIMESTAMP Y For REFRESH = 'D' or 'O', time at which the data was last refreshed (REFRESH TABLE statement); null value otherwise.LOCKSIZE CHAR(1)Indicates the preferred lock granularity for tables that are accessed by data manipulation language (DML) statements. Applies to tables only. Possible values are:I = Block insertR = RowT = TableBlank = Not applicableInitial value is 'R'.VOLATILE CHAR(1)C = Cardinality of the table is volatile Blank = Not applicableROW_FORMAT CHAR(1)Not used.PROPERTY VARCHAR(32)Properties for a table. A single blank indicates that the table has no properties.STATISTICS_PROFILE CLOB(10M)Y RUNSTATS command used to register a statistical profile for the object.COMPRESSION CHAR(1)B = Both value and row compression are activatedN = No compression is activated; a row format that does not support compression is usedR = Row compression is activated; a row format that supports compression might be usedV = Value compression is activated; a row format that supports compression is usedBlank = Not applicableACCESS_MODE CHAR(1)Access restriction state of the object. These states only apply to objects that are in set integrity pending state or to objects that were processed by a SET INTEGRITY statement. Possible values are:D = No data movementF = Full accessN = No accessR = Read-only accessCLUSTERED CHAR(1)Y Y = Table is multidimensionally clustered (even if only by one dimension)Null value = Table is not multidimensionally clusteredACTIVE_BLOCKS BIGINT Total number of active blocks in the table, or -1. Applies to multidimensional clustering (MDC) tables only.DROPRULE CHAR(1)N = No ruleR = Restrict rule applies on dropMAXFREESPACESEARCH SMALLINT Reserved for future use. Column Name Data Type Nullable DescriptionMAXFREESPACESEARCH SMALLINT Reserved for future use.AVGCOMPRESSEDROWSIZE SMALLINT Average length (in bytes) of compressed rows in this table; -1 if statistics are not collected.AVGROWCOMPRESSIONRATIO REAL For compressed rows in the table, this is the average compression ratio by row; that is, the average uncompressed row length divided by the average compressed row length; -1 if statistics are not collected.AVGROWSIZE SMALLINT Average length (in bytes) of both compressed and uncompressed rows in this table; -1 if statistics are not collected.PCTROWSCOMPRESSED REAL Compressed rows as a percentage of the total number of rows in the table; -1 if statistics are not collected.LOGINDEXBUILD VARCHAR(3)Y Level of logging that is to be performed during create, recreate, or reorganize index operations on the table.OFF = Index build operations on the table will belogged minimallyON = Index build operations on the table will belogged completelyNull value = Value of the logindexbuild databaseconfiguration parameter will be used to determinewhether or not index build operations are to becompletely loggedCODEPAGE SMALLINT Code page of the object. This is the default code page used for all character columns, triggers, check constraints, and expression-generated columns.ENCODING_SCHEME CHAR(1)A = CCSID ASCII was specifiedU = CCSID UNICODE was specified Blank = CCSID clause was not specifiedPCTPAGESSAVED SMALLINT Approximate percentage of pages saved in the table as a result of row compression. This value includes overhead bytes for each user data row in the table, but does not include the space that is consumed by dictionary overhead; -1 if statistics are not collected.LAST_REGEN_TIME TIMESTAMP Time at which any views or check constraints on the table were last regenerated.SECPOLICYID INTEGER Identifier for the security policy protecting the table; 0 for non-protected tables.PROTECTIONGRANULARITY CHAR(1)B = Both column- and row-level granularityC = Column-level granularityR = Row-level granularityBlank = Non-protected tableDEFINER1VARCHAR(128)Authorization ID under which the table, view, alias, or nickname was created.REMARKS VARCHAR(254)Y User-provided comments, or null. Notes:1. The DEFINER column is included for backwards compatibility. See OWNER.Column Name Data Type Nullable Description。

the z-score and the standard normal table

the z-score and the standard normal table第一节讲了probability的概念和隐藏的一个前提，random sampling。

random sampling又分为random sampling with replacement (independent random sampling)和random sampling without replacement。

最后讲了probability和frequency distributions的关联，就在于，probabilities and proportions are equivalent。

第二节开始，在之前（第二章）作为一个宋兵甲出现过的小角色normal distribution开始隆重登场了。

因为normal distribution是可以用方程来表示的，还可以求面积。

而面积意味着可以计算分布其中的数值的比例，比例意味着probability的计算。

这里又有一个现成的表格，the unit normal table，可以辅助你计算面积或是概率。

The unit normal table lists relationships between z-score locations and proportions in a normal distribution…Similarly, if you know th proportions, you can use the table to find the specific z-score location.具体细节不再多说。

第三节是深入第二节的内容，各种计算问题。

前三节实际上都是理论，第四节讲的是应用。

probability, proportion, normal distribution, the unit normal table的具体应用，体现在binomial distribution上。

Ecopath with Ecosim和Et-diagnosis用户指南说明书

Examples
data(ecopath_guinee) #Impacts of global changes in fishing efforts multipliers (in the range 0-5) create.ETdiagnosis(create.ETmain(ecopath_guinee),same.mE=TRUE) #Test of all the combinations of fishing effort multipliers per fleet #(in the range 0-5) create.ETdiagnosis(create.ETmain(ecopath_guinee)) #With biomass input control create.ETdiagnosis(create.ETmain(ecopath_guinee),B.Input=TRUE) #Impacts of changing fishing effort against Barracudas+ and Carangids groups
- Variables characterizing the state and functioning of the modeled ecosystem: biomass, ﬂow, kinetic, catches (total and per ﬂeet) and ﬁshing mortality per trophic level.
is a parameter of the create.smooth function. It deﬁnes the value of the constant sigma of the lognormal distribution for smooth_type=1. By default, sigmaLN_cst=0.12.

gretlR 0.1.4 用户指南说明书

Package‘gretlR’October13,2022Type PackageTitle A Seamless Integration of'Gretl'and'R'Version0.1.4Maintainer Sagiru Mati<***************.ng>Description It allows running'gretl'(</index.html>)pro-gram from R,R Markdown and Quarto.'gretl'('Gnu'Regression,'Econometrics',and Time-series Library)is a statistical software for Econometric analysis.This package does not only in-tegrate'gretl'and'R'but also serves as a'gretl'Knit-Engine for'knitr'pack-age.Write all your'gretl'commands in'R',R Markdown chunk.Depends R(>=3.6.0)Imports knitr(>=1.20),rmarkdown,kableExtra,magrittrSystemRequirements gretl(>=1.9.4)License GPLURL https:///package=gretlRBugReports https:///sagirumati/gretlR/issuesEncoding UTF-8VignetteBuilder knitrRoxygenNote7.1.2NeedsCompilation noRepository CRANDate/Publication2022-05-0115:40:05UTCAuthor Sagiru Mati[aut,cre](<https:///0000-0003-1413-3974>)R topics documented:gretlR-package (2)eng_gretl (2)exec_gretl (4)exec_inp (5)1import_kable (6)include_graph (8)include_tex (9)write_inp (10)Index12gretlR-package gretlR:A Seamless Integration of’Gretl’and’R’DescriptionIt allows running’gretl’(</index.html>)program from R,R Markdownand Quarto.’gretl’(’Gnu’Regression,’Econometrics’,and Time-series Library)is a statisticalsoftware for Econometric analysis.This package does not only integrate’gretl’and’R’but alsoserves as a’gretl’Knit-Engine for’knitr’package.Write all your’gretl’commands in’R’,RMarkdown chunk.Author(s)Maintainer:Sagiru Mati<***************.ng>(ORCID)See AlsoUseful links:•https:///package=gretlR•Report bugs at https:///sagirumati/gretlR/issuesOther important functions:eng_gretl(),exec_gretl(),exec_inp(),import_kable(),include_graph(), include_tex(),write_inp()eng_gretl Add gretl as knit-engine to knitr packageDescriptionThis package runs on top of knitr to facilitate communication with gretl.Run gretl scripts fromR,R Markdown and Quarto document.Usageeng_gretl(options)Argumentsoptions Chunk options,as provided by knitr during chunk execution.Chunk option forthis is gretlDetailsThe gretl engine can be activated viaknitr::knit_engines$set(gretl=gretlR::eng_gretl)This will be set within an R Markdown document’s setup chunk.ValueSet of gretl(open-source software for Econometrics)codesAuthor(s)Sagiru Mati,ORCID:0000-0003-1413-3974•Yusuf Maitama Sule(Northwest)University Kano,Nigeria•SMATI AcademyReferencesBob Rudis(2015).Running Go language chunks in R Markdown(Rmd)ﬁles.Available at:https:///hrbrmstr/9a Yihui Xie(2019).knitr:A General-Purpose Package for Dynamic Report Generation in R.Rpackage version1.24.Yihui Xie(2015)Dynamic Documents with R and knitr.2nd edition.Chapman and Hall/CRC.ISBN978-1498716963Yihui Xie(2014)knitr:A Comprehensive Tool for Reproducible Research in R.In Victoria Stodden,Friedrich Leisch and Roger D.Peng,editors,Implementing Reproducible Computational Research.Chapman and Hall/CRC.ISBN978-1466561595See AlsoOther important functions:exec_gretl(),exec_inp(),gretlR,import_kable(),include_graph(),include_tex(),write_inp()Examplesknitr::knit_engines$set(gretl=gretlR::eng_gretl)library(gretlR)4exec_gretl exec_gretl Execute gretl codes in RDescriptionUse this function to Execute gretl codes in R.Usageexec_gretl(code,path=basename(tempfile("gretlR")))Argumentscode Object or a character string representing the set of gretl codespath Object or a character string representing the directory to execute the gretl codes(default:gretlR)ValueSet of gretl(open-source software for Econometrics)outputsSee AlsoOther important functions:eng_gretl(),exec_inp(),gretlR,import_kable(),include_graph(), include_tex(),write_inp()Exampleslibrary(gretlR)##Not run:code=r (nulldata500set seed13gretl1=normal()gretl2=normal()setobs121980:01--time-seriesgnuplot gretl1--time-series--with-lines--output="line.png"gnuplot gretl2gretl1--output="scatter.png")exec_gretl(code)##End(Not run)exec_inp5 exec_inp Execute existing gretl inpﬁle(s)in RDescriptionUse this function to execute existing gretl inpﬁle(s)in RUsageexec_inp(path=".")Argumentspath Object or a character string representing the path(s)to the gretlﬁle(s).(default:".")ValueSet of gretl(open-source software for Econometrics)outputsSee AlsoOther important functions:eng_gretl(),exec_gretl(),gretlR,import_kable(),include_graph(), include_tex(),write_inp()Exampleslibrary(gretlR)##Not run:code=r (nulldata500set seed13gretl1=normal()gretl2=normal()setobs121980:01--time-seriesgnuplot gretl1--time-series--with-lines--output="line.png"gnuplot gretl2gretl1--output="scatter.png")write_inp(code,path="SomeFolder/gretlCodes")exec_inp("SomeFolder/gretlCodes")##End(Not run)import_kable Importﬁle as kable in R Markdown or Quarto document.DescriptionUse this function to importﬁle as kable in R Markdown or Quarto document.Usageimport_kable(path=".",chunk="",file="",start=NA,end=NA,skip_blank=TRUE,format=kable_format(),digits=getOption("digits"),s=NA,s=NA,align, caption=NULL,label=NULL,format.args=list(),escape=FALSE,table.attr="",booktabs=TRUE,longtable=FALSE,valign="t",position="h",centering=TRUE,vline=getOption("knitr.table.vline",if(booktabs)""else"|"), toprule=getOption("knitr.table.toprule",if(booktabs)"\\toprule"else"\\hline"),bottomrule=getOption("knitr.table.bottomrule",if(booktabs)"\\bottomrule"else"\\hline"),midrule=getOption("knitr.table.midrule",if(booktabs)"\\midrule"else"\\hline"),linesep=if(booktabs)c("","","","","\\addlinespace")else"\\hline",caption.short="",table.envir=if(!is.null(caption))"table",...)Argumentspath Object or a character string representing the path(s)to the TeX(default:".")chunk Name of the gretl chunk that generates the TeXﬁle.file Name of aﬁle to be imported as kablestart Numeric.The start line of the TeXﬁle to include.end Numeric.The last line of the TeXﬁle to include.skip_blank Logical.Whether or not to include blank rows.format A character string.Possible values are latex,html,pipe(Pandoc’s pipe tables),simple(Pandoc’s simple tables),and rst.The value of this argument will beautomatically determined if the function is called within a knitr document.Theformat value can also be set in the global option knitr.table.format.Ifformat is a function,it must return a character string.digits Maximum number of digits for numeric columns,passed to round().This canalso be a vector of length ncol(x),to set the number of digits for individualcolumns.s Logical:whether to include row names.By default,row names are included ifrownames(x)is neither NULL nor identical to1:nrow(x).s A character vector of column names to be used in the table.align Column alignment:a character vector consisting of l (left), c (center)and/or r (right).By default or if align=NULL,numeric columns are right-aligned,and other columns are left-aligned.If length(align)==1L,the stringwill be expanded to a vector of individual letters,e.g. clc becomes c( c ,l , c ),unless the output format is LaTeX.caption The table caption.label The table reference label.By default,the label is obtained from knitr::opts_current$get( label ).To disable the label,use label=NA.format.args A list of arguments to be passed to format()to format table values,e.g.list(big.mark= , ).escape Boolean;whether to escape special characters when producing HTML or LaTeXtables.When escape=FALSE,you have to make sure that special characters willnot trigger syntax errors in LaTeX or HTML.table.attr A character string for addition HTML table attributes.This is convenient if yousimply want to add a few HTML classes or styles.For example,you can put’class="table"style="color:red"’.booktabs T/F for whether to enable the booktabs format for tables.I personally wouldrecommend you turn this on for every latex table except some special cases.longtable T/F for whether to use the longtable format.If you have a table that will spanover two or more pages,you will have to turn this on.valign You probably won’t need to adjust this latex option very often.If you are familarwith latex tables,this is the optional position for the tabular environment con-troling the vertical position of the table relative to the baseline of the surroundingtext.Possible choices are b,c and t(default).position This is the"real"or sayﬂoating position for the latex table environment.Thekable only puts tables in a table environment when a caption is provided.Thatis also the reason why your tables will beﬂoating around if you specify captionsfor your table.Possible choices are h(here),t(top,default),b(bottom)and p(on a dedicated page).centering T(default)/F.Whether to center tables in the table environment.vline vertical separator.Default is nothing for booktabs tables but"|"for normal ta-bles.toprule toprule.Default is hline for normal table but toprule for booktabs tables.bottomrule bottomrule.Default is hline for normal table but bottomrule for booktabs tables.midrule midrule.Default is hline for normal table but midrule for booktabs tables.linesep By default,in booktabs tables,kable insert an extra space everyﬁve rows forclear display.If you don’t want this feature or if you want to do it in a dif-ferent pattern,you can consider change this option.The default is c(”,”,”,”,’\addlinespace’).Also,if you are not using booktabs,but you want a cleanerdisplay,you can change this to”.caption.short Another latex feature.Short captions for tablestable.envir You probably don’t need to change this as well.The default setting is to put atable environment outside of tabular if a caption is provided....Other arguments(see Examples and References).8include_graphValuekableSee AlsoOther important functions:eng_gretl(),exec_gretl(),exec_inp(),gretlR,include_graph(), include_tex(),write_inp()Exampleslibrary(gretlR)##Not run:code=r (nulldata500set seed13gretl1=normal()gretl2=normal()setobs121980:01--time-seriesols gretl1const gretl2tabprint--output="olsTable.csv")exec_gretl(code=code,path= gretlR/Table/gretlCode )#this creates gretlR/Table folderimport_kable(chunk="Table",file="olsTable.csv",format="pandoc",caption="Table generated from gretl chunk",start=3,end=7,digits=2)#Alternatively,use the absolute/relative path to the fileimport_kable(path="gretlR/Table/olsTable.csv",format="pandoc",caption="Table generated from path",start=3,end=7,digits=2)##End(Not run)include_graph Include graphﬁle in R Markdown or Quarto document.DescriptionUse this function to include graphﬁle in R Markdown or Quarto document.Usageinclude_graph(path=".",chunk="",graph="")Argumentspath Object or a character string representing the path(s)to the TeX(default:".") chunk Name of the gretl chunk that generates the TeXﬁle.graph Name of the graph and its extensioninclude_tex9ValueSet of gretl(open-source software for Econometrics)outputsSee AlsoOther important functions:eng_gretl(),exec_gretl(),exec_inp(),gretlR,import_kable(), include_tex(),write_inp()Exampleslibrary(gretlR)##Not run:code=r (nulldata500set seed13gretl1=normal()gretl2=normal()setobs121980:01--time-seriesgnuplot gretl1--time-series--with-lines--output="line.png")exec_gretl(code)include_graph(path="line.png")##End(Not run)include_tex Include TeXﬁle in R Markdown or Quarto document.DescriptionUse this function to include TeXﬁle in R Markdown or Quarto document.Usageinclude_tex(path=".",chunk="",tex="",start=NA,end=NA)Argumentspath Object or a character string representing the path(s)to the TeX(default:".") chunk Name of the gretl chunk that generates the TeXﬁle.tex Name of a LaTeXﬁlestart Numeric.The start line of the TeXﬁle to include.end Numeric.The last line of the TeXﬁle to include.ValueSet of gretl(open-source software for Econometrics)outputs10write_inpSee AlsoOther important functions:eng_gretl(),exec_gretl(),exec_inp(),gretlR,import_kable(), include_graph(),write_inp()Exampleslibrary(gretlR)##Not run:code=r (nulldata500set seed13gretl1=normal()gretl2=normal()setobs121980:01--time-seriesols gretl1const gretl2tabprint--output="olsTable.tex")exec_gretl(code=code,path= gretlR/TeXFolder/gretlCode )include_tex(chunk="TeXFolder",tex="olsTable")#Alternatively,use the absolute/relative path to the TeX fileinclude_tex("gretlR/TeXFolder/olsTable.tex")##End(Not run)write_inp Write gretl inpﬁle in RDescriptionUse this function to write gretl inpﬁle in RUsagewrite_inp(code,path)Argumentscode Object or a character string representing the set of gretl codespath Object or a character string representing the path to write the gretl inpﬁle. ValueSet of gretl(open-source software for Econometrics)outputsSee AlsoOther important functions:eng_gretl(),exec_gretl(),exec_inp(),gretlR,import_kable(), include_graph(),include_tex()write_inp11Exampleslibrary(gretlR)##Not run:code=r (nulldata500set seed13gretl1=normal()gretl2=normal()setobs121980:01--time-seriesgnuplot gretl1--time-series--with-lines--output="line.png"gnuplot gretl2gretl1--output="scatter.png")write_inp(code,path="gretlCodes")##End(Not run)Index∗documentationeng_gretl,2exec_gretl,4exec_inp,5gretlR-package,2import_kable,6include_graph,8include_tex,9write_inp,10∗important functionseng_gretl,2exec_gretl,4exec_inp,5gretlR-package,2import_kable,6include_graph,8include_tex,9write_inp,10eng_gretl,2,2,4,5,8–10exec_gretl,2,3,4,5,8–10exec_inp,2–4,5,8–10format,7gretlR,3–5,8–10gretlR(gretlR-package),2gretlR-package,2import_kable,2–5,6,9,10include_graph,2–5,8,8,10include_tex,2–5,8,9,9,10opts_current,7write_inp,2–5,8–10,1012。

食品科学导论课后题

Chapter 1Overview of Food ScienceReview Questions (P18)1.Away-from-home meals captures 45 percent of the U.S. food dollar. (P10)2.Why have the international activities of food industries increased? (P16)Aside from the worldwide demand for food and food products, the recent trends to decrease trade tariffs has stimulated the international activities in the food industry.Improvements in transportation and communication have also increased the international activities of food industries. all seven product lines along which the food industry is divided. (P4)Cereal and bakery productsMeat, fish, and poultryDairy productsFruits and vegetablesSugars and other sweetsFats and oilsNonalcoholic beverages/alcoholic beverages4.List the four artificial divisions of the food industry. (P4)ProductionManufacturing/processingDistributionMarketing5.Consumption of cheese has increased, whereas consumption of red meat has declined overthe last 27 years. (P17)6.List four reasons that influence people and the kind of food they eat. (P17)The kinds of foods people eat change in response to many influences, such as demographic shifts; supply of ingredients; availability and costs of energy; politics; scientific advances in nutrition, health, and food safety; and changes in lifestyle.7.About 10000 new food products are introduced each year. (P17)8.Explain how the consumer votes in the marketplace. (P3)Consumers vote every day in the marketplace with their dollars.9.Define an allied industry. (P11)An allied industry produces nonfood items that are necessary for marketing food.pare the spending on food in the United States to that of Spain and Greece. (P6-7) Americans spent only about 8 percent of their personal consumption expenditures for food to be eaten at home. This compares with 18 percent for Spain and 32 percent for Greece. Chapter 2Review of Chemistry (P31)1.The atom is the smallest unit of an element that still exhibits the properties of that element.(P21)2.Define a molecule. (P26)A molecule is the smallest identifiable unit into which a pure substance can be divided and still retain the composition and chemical properties of that substance. and describe the two divisions of metabolism. (P28)Anabolism, reactions involving the synthesis of compounds.Catabolism, reactions involving the breakdown of compounds.4.List the elements most important to life. (P22)The elements important to life include carbon, hydrogen, nitrogen, and oxygen.5.How are covalent bonds formed? (P22)Covalent bonds are formed by the sharing of a pair of electrons.6.The atomic number of an atom is the total number of protons. The atomic weight of an atomis the total number of protons plus neutrons. (P21)7.Salt is an example of a/an ionic bond. (P25)8.Explain the oxidation-reduction reaction. (P26)The rusting of metals, the process involved in photography, the way living systems produce and use energy, and the operation of a car battery are but a few examples of oxidation-reduction reactions.9.Chemical properties of an element are determined by the number of electrons in theoutermost energy level of an atom. (P22)10.All carbon atoms have four bonds to account for. What are the names of the bonds? (P29) Each carbon can connect to another carbon, a hydroxyl, a hydrogen, an amino group, an oxygen.Carbon-carbon bonds; carbon-hydroxyl bonds, carbon-hydrogen bonds, carbon-amino bonds; carbon-oxygen bonds.Chapter 3 Chemistry of Foods (P62)1.What is the chemical composition of a carbohydrate? (P34)A carbohydrate is composed of carbon and water and have a composition of C n(H2O)n.2.List the three functions of proteins in food. (P48)Proteins contribute to the color, texture, and flavor of foods.3.What is the difference between a monosaccharide and a disaccharide? (P35)A monosaccharide may have 5 or 6 carbons. A disaccharide is made of two monosaccharides. five functions carbohydrates play in foods. (P34-35)Carbohydrates enhance flavor, contribute to texture, prevent spoilage, influence color, and give structure.Flavor enhancing and sweetening due to caramelization Water binding Contributing to texture Hygroscopic nature/water absorption Providing source of yeast food Regulating gelation of pectin dispersing molecules of protein or starch Acting to subdivide shortening for creaming control crystallization Preventing spoilage Delaying coagulation protein Giving structure due to crystals Affecting osmosis Affecting color of fruits Affecting texture (viscosity, structure) Contributing flavor other than sweetness5.Explain two functions of water in the body. (P58)Carries nutrients and wastesn Maintains structure of molecules Participates in chemical reactions Acts as a solvent for nutrients Lubricates and cushions joints, spinal cord, and fetus (during pregnancy) Helps regulate body temperature Maintains blood volume6.Triglycerides, fatty acids, phospholipids, some pigments, some vitamins, and cholesterol areclassed as lipids. (P48)7.Fatty acid molecules that are unsaturated contain what are known as double bonds. A fattyacid that contains one double bond is called mono- unsaturated. Fatty acids that contain two or more double bonds are called polyunsaturated. (P50)8.List the fat- and water-soluble vitamins. (P53)Fat soluble vitamins include vitamins A, D, E, and K.The water-soluble vitamins include the B vitamins and vitamin C.9.Choline is part of several major phospholipids critical for normal membrane structure andfunction, is used by the kidney to maintain water balance, and is used to produce the important neurotransmitter acetylcholine. (P59) ten minerals important in nutrition. (P55)Microminerals important in nutrition include:Chromium Cobalt Copper Fluorine Iodine Iron Manganese Molybdenum Nickel Selenium Silicon Tin Vanadium ZincChapter 4 Nutrition and digestion (P79-80) six minerals required by the body. (P73)Calcium; Phosphorus; Iron; Copper; Magnesium; Sodium; Potassium; Chloride; Zinc; Iodine; Manganese; Selenium.2.Identify the protein requirement for a 19-year-old male and female. (P68)Protein needs is about 61 grams per day for a 19-year-old male and is 44 grams per day for a female at the same age.3.Describe the function of protein in diet. (P69)Protein provides essential amino acids, and nitrogen for the synthesis of other nitrogen-containing compounds.Enough protein in the diet can prevent the dietary diseases kwashiorkor or marasmus. Protein provides essential amino acids.Protein also provides nitrogen for the synthesis of purines, pyrimidines, porphyrin in nucleic acids, ATP, hemoglobin, and cytochromes.Enough protein in the diet of people can prevent the dietary diseases kwashiorkor or marasmus.4.How many calories are in 1 gram of protein, carbohydrate, fat, and alcohol? (P65)Proteins and carbohydrates provide about 4 calories per gram. Fat contributes about 9 calories per gram. Alcohol supplies about 7 calories per gram.5.Linoleic acid is an essential fatty acid. (P71)6.Identify the organ of digestion that receives enzymes from the pancreas. (P76)The small intestine receives enzymes from the pancreas.7.During digestion, enzyme such as aminopeptidase, carboxypeptidases, and dipeptidaseconvert polypeptides into amino acids. (P77)8.What nutritional deficiency causes kwashiorkor and marasmus? (P69)Protein deficiencies can lead to kwashiorkor or marasmus.9.List five essential amino acids. (P69)Phenylalanine; Tryptophan; Histidine; Valine; Leucine; Isoleucine; Lysine; Methionine; Threonine; Arginine10.What factor determines protein quality? (P69)Ratios of essential amino acid.Chapter 5Food composition (P87)1.How many Calories and grams of protein are in 3 oz. of Froot Loops ®cereal? (P578)330 kilocalories (Calories) and 6 grams of protein are in 3 oz. of Froot Loops ®cereal.2.How many grams of fat are in one slice of cheese pizza? (P588)9 grams of fat are in one slice of cheese pizza.3.Describe item #4270. (P580)3 grams of water, 185 kilocalories, 2 grams of protein, 11 grams of fat, 18 milligrams of cholesterol, 26 grams of carbohydrate, 13 milligrams of calcium, 34 milligrams of phosphorous, 1 milligram of iron, 82 milligrams of potassium, 82 milligram of Sodium, 20 IU of V A, 0.06 milligrams of thiamin, 0.06 milligrams of riboflavin, and 0.6 milligrams of niacin are in 4 chocolate chip cookies.3g water, 185 Cal, 2g protein, 11g fat, 18mg cholesterol, 26g carbohydrate, 13mg Ca, 34 mg P, 1mg Fe, 82mg K, 82mg Na, 20 IU V A, 0.06mg thiamin, 0.06mg riboflavin, and 0.6mg niacin are in 4 chocolate chip cookies.4.List three methods for determining the composition of food. (P83)The methods for determining the composition of food are spectrophotometry, liquid chromatography, and gas chromatography.5. A small calorie is defined as the amount of heat required to raise the temperature of one gramof water one ℃. (P84)6.Describe two uses of a food composition table. (P86)Food composition tables are used to evaluate the nutritional value of food supplies, to develop food distribution programs, to plan and evaluate food consumption surveys, to provide nutritional counseling, and to estimate the nutritional content of individual diets.Food composition tables are used to evaluate diets and food supplies. four factors that affect the nutrient content of foods. (P83)Nutrient content of foods is influenced by variety, season, geographical differences, stage of harvesting, handling, commercial processing, packaging, storage, display, home preparation, cooking, and serving.8.Explain the relationship between Calorie, Kcal, calorie, and cal. (P84)A Calorie is a metric unit of heat measurement. The small calories (cal) is the amount of heat required to raise the temperature of 1 gram of water from 14.5° to 15.5 ℃.A large calorie, or kilocalorie (Cal), usually referred to as a calorie and sometimes as a kilogram calorie, equals 1000 cal.9.Identify the following abbreviations: oz, mg, IU, RE, mono, sat, poly, carb, chols. (P86)Oz=ounce, mg=miligram, IU=International Unit, RE=Retinol Equivalent, mono=monounsaturated, sat=saturated, poly=polyunsaturated, carb=carbohydrate, chols=cholesterol.10.In terms of energy and protein, what is the difference between a slice of white bread and aslice of whole wheat bread?(P576)A slice of white bread provides less energy and protein than a slice of whole wheat bread does.Chapter 6 Quality factors in foods (P107)1.List three components of reflected light used to define colors. (P91)Value, hue, and chroma. one instrument used to measure texture. (P93-94)Compressimeter—determine the compressibility of cakes and other “spongelike ” products; Penetrometer—measure gel strength;Warner-Bratzler shear apparatus—evaluating meat tenderness;Brookfield viscometer—measure the viscosity;Succulometer;Tenderometer.3.Discuss what humans can taste and what they smell and how this forms food flavor. (P95) Humans can taste sweet, salty, sour, and bitter and smell fruity, astringency, sulfur, hot. Food flavor is a combination of taste and smell.4.Identify the following acronyms: AMS, HACCP, TQM, GMP, CID. (P99, 104-106) AMS—the Agricultural Marketing ServiceHACCP—Hazard Analysis and Critical Control PointTQM—Total Quality ManagementGMP—Good Manufacturing PracticesCID—Commercial Item Descriptions5.Industry and AMS develop and maintain CIDs. (P99)6.List six factors that can influence the flavor of food. (P96)Depending on the food, flavor can be influenced by bacteria, yeasts, molds, enzymes, heat/cold, moisture/dryness, light, time, additives.7.Changes in the texture of food are often due to water status. (P94)8.What qualities do consumers expect of their food? (P106)Consumers expect certain qualities from their food. These include color, flavor, texture, and even size.9.The study of the science of the deformation of matter is called rheology. (P93)10.How do fats or lipids affect the texture of food? (P97)Lipids (fats) are softeners and lubricants used in cakes.Chapter 7 Unit operations in food processing (P122-123)1.The manufacture of ice cream is an example of a/an swept surface heat exchanger. (P117)2.Why are foods packaged? (P120)Packaging is used for a variety of purpose including shipping, dispensing, improving the usefulness of the product, and protection from microbial contamination, dirt, insects, light, moisture, drying, flavor changes, and physical alterations.Attractive packaging also helps with marketing of the food product.3.Specific heat is the amount of heat required to change the temperature of a unit mass ofproduct a specific temperature without changing the material. (P115) the three methods for separating foods. (P111-113)Three methods for separating foods are cream separator, clarification, and membrane processes.5.What are the two types of fluid flow pumps? (P114)Centrifugal pump and positive pump are two types of fluid flow pumps.6.Plate heat exchanges pass fluid over a plate where a heating or cooling medium is beingpassed up or down on the other side of the plate. (P116)7.List the four factors affecting the mixing of food products. (P114)Factors affecting the mixing of food are design of impeller, diameter of impeller, speed, and baffles.8.Why is it important to handle food materials carefully? (P110)To maintain sanitary conditions, minimize losses, maintain quality, and minimize bacterial growth.9.Explain the three common methods of drying foods. (P119)Three common methods of drying are sun or tray drying, spray drying, and freeze drying. 10.List three membrane processes for separating food products. (P112)Reverse osmosis, ultrafiltration, and microfiltration.Chapter 8 Food deterioration (P136) the two environmental conditions that affect microbial growth on food. (P127) Environmental conditions that affect microbial growth include temperature and oxygen. the three general categories of food deterioration. (P125)The three general categories of food deterioration are: physical, chemical, and biological.3.Some of the post harvest enzymes are desirable in food preservation. (P136)4.Why do foods have a shelf life? (P136/125)All foods undergo deterioration. All foods have a time limit of their usefulness—shelf life. 5.The growth of aerobes is slowed by removing the oxygen; while providing oxygen limits thegrowth of anaerobes. (P135)6.List four factors that cause food deterioration. (P125)Factors that cause food deterioration are many, including light, cold heat, oxygen, moisture, dryness, othertypes of radiation, enzymes, microorganisms, time, industrial contaminants, and macroorganisms (insects, mice, and so on).7.What is a food-borne disease? (P127)Food-borne disease is any disease resulting from the consumption of food.8.Give four preservation techniques to prevent food deterioration. (P132-135)Food preservation involves the use of heat, cold, drying, acid, sugar and salt, smoke, atmosphere, chemicals, radiation, and mechanical methods.9.Why are some fruits and vegetables washed immediately after being picked? (P128)Some fruits and vegetables are washed to remove internal heat and cool immediately after being picked in order to minimize post-harvest biochemical changes. four food enzymes and describe their function. (P129-131)Ascorbic acid oxidase, oxidize ascorbic acid to dehydro form destroying the browning prevention ability.Beta-amylase, with fungal glucoamylase produces mixtures of fermentable sugars: glucose, maltose.Bromelain, acts on collagen to hydrolyze peptides, amides, and esters from the non-reducing end.Catalase, removes residual H2O2 treated foods, converts H2O2 to H2O and oxygen.Chapter 9 Heat (P154)1.The most heat resistant microbe in canned foods is Clostridium botulinum. (P144)2.What are the two main objectives of pasteurization? (P143)Destroy all pathogenic microorganisms that might grow in a specific product;Extension of shelf life by decreasing number of spoilage organisms present. four types of preservatives achieved by heating. (P142)Sterilization, commercial sterility, pasteurization, and blanching.4.In the thermal death curve, the D value relates to the time to reduce the number ofmicroorganisms, and the Z value relates to the temperature required to decrease the microorganisms. (P148)5.Heating before packaging requires what type of packaging? (P148)Heating after packaging requires aseptic (germ-free) packaging.6.Conduction heating is thermal transfer due to collisions of hot food particles with cooler ones.(P145)7.What is the difference between a still retort and an agitating retort? (P149)In the still retort process, the product is placed in a container and then heated in steam atmosphere without agitation.In the agitating retorts the product is agitated during cooking.8.Identify the two factors to pick the right heat treatment severity for a specific food. (P143)To pick the right heat treatment severity for a specific food, two factors must first be determined:Time-temperature combination required to inactivate the most resistant microbe;Heat penetration characteristics of the food and the container.9.Define conduction heating. (P145)Conduction heating is thermal transfer due to collisions of hot food particles with coolerones.10.Radiation is the transfer of energy in the form of electromagnetic waves. (P145)Chapter 10 Cold (P169-170) the three methods of freezing. (P164)Freeze the product in air;Freeze the product with directly contact;Immersion freezing.2.List the four requirements of refrigerated storage. (P159)Refrigerated storage requires low temperatures, air circulation, humidity control, and modified gas atmosphere.3.Identify four changes in food during refrigeration. (P159)During refrigerated storage, foods can experience chill injury, flavor absorption, and loss of firmness, color, flavor, and sugar.4. A key factor in food freezing is how quickly the food is frozen. (P163)5.Describe the temperature difference between cooling, refrigeration, and freezing. (P157) Cooling: temperature from 68˚ to 28˚F (16˚ to -2 ˚C);Refrigeration: temperature from 40˚ to 45˚F (4.5˚ to 7 ˚C);Freezing: temperature from 32˚ to 0˚F (0˚ to -18˚C).6.Why do food processors blanch vegetables prior to freezing them? (P160)Enzymes will maintain a certain level of activity during freezing. the two types of containers for home freezing use. (P165)Rigid containers and flexible bags or wrappings.8.Freezing cannot improve the flavor or texture of any food. (P167)9.Explain why a freezer should not be overloaded with unfrozen food. (P167)Overloading slows down the freezing rate, and foods that freeze too slowly may lose quality.10.List the three things packaging for frozen foods protects against. (P165)Packaging for frozen foods protects against dehydration, light, and air.Chapter 11 Drying and dehydration (P187)1.List the three drying methods. (P177)Common drying methods are: air convection, drum, vacuum, freeze.2.Dehydration results in decreased weight and volume of a product a nd shipping costs. (P186)3.Vacuum drying produces the highest quality of product by is also very costly. (P178)4.What is ultrafiltration? (P182)Ultrafiltration is a membrane filtration process operating at 2 to 10 bars pressure and allowing molecules the size of salts and sugars to pass through the membrane pores, while molecules the size of proteins are rejected.5.The principle of freeze-drying is that under conditions of low vapor pressure (vacuum), waterevaporates from ice without the ice melting. (P178)6.The purpose of drying is to remove enough moisture to prevent microbial growth. (P173)7.Define sublimation. (P178)Water goes from a solid to a gas without passing through the liquid phase. This is called sublimation.8.What types of foods are dried using a drum or roller driers? (P177)Drum or roller driers are used for drying liquid foods, purees, pastes, and mashes.9.Discuss the two problems with drying of a food product. (P173)Dried foods are not sterile. Many spores survive in dry areas of food.Drying never completely removes all water.10.List three chemical changes that occur during drying. (P175-176)Several chemical changes can occur during drying, including: caramelization, enzymatic browning, nonenzymatic browning, loss of ease of rehydration, loss of flavor.Chapter 12 Radiant and electrical energy (P197)1.Describe ohmic heating. (P196)Ohmic heating is the heating of a food product by using an alternating current flowing between two electrodes. the two requirements for irradiation. (P190)Two requirements for the irradiation process include:A source of radiant energy;A way to confine that energy.3.Radiation is broadly defined as energy moving through space in invisible waves. (P190)4.Explain ionizing radiation. (P190)Ionizing radiation, also known as irradiation, is a method of food preservation. These shorter wavelengths are capable of damaging microorganisms.5.List the four ways in which irradiation is most useful. (P192)Irradiation is most useful in four areas: preservation; sterilization; control of sprouting, ripening, and insect damage, and control of food borne illness.6.Describe how microwaves heat food. (P197)Microwaves heat foods by generating heat inside the food due to water friction.7.When salt is added to water, it changes the microwave heating characteristics in two differentdirections. (P195)8.List three specific ways irradiation has been approved for use by the FDA. (P191-192)For eliminating insects from wheat, potatoes, flour, spices, tea, fruits, and vegetables.To control sprouting and ripening.Use irradiation on pork to control trichinosis.To control Salmonella and other harmful bacteria in chicken, turkey, and other fresh and frozen uncooked poultry.To control pathogens in fresh and frozen red meats such as beef, lamb, and pork.9.Food composition influences microwave heating of food in what two ways? (P195)Food composition does not only influence the loss factor, but also penetration depth.10.Irradiation cannot be used on what two specific products? (P192)Irradiation cannot be used with dairy products and some fruits, such as peaches and nectarines.Chapter 24 Environmental Concerns and ProcessingReview Questions (P448-449)1.Water serves as a universal solvent. (P440)2.List five methods of conserving water during food processing. (P447)Always treat water as a raw material with a real cost; Set water conservation goals for the plant; Make water conservation a management priority; Install water meters and monitor water use; Train employees how to use water efficiently; Use automatic shut-off nozzles onall water hoses; Use high-pressure, low volume cleaning systems; Do not let people use water hoses as brooms; Reuse water where possible; Minimize spills of ingredients and of raw and finished product on the floor; Always clean up the spills before washing.总是把水看成是有成本的原料，制定工厂的节水目标，使节水成为管理首要考虑的内容，安装水表管理水的使用，培训员工怎样有效用水，在所有水管上安装自动关水喷嘴，使用高压低量的清洁系统，不允许用水管冲洗，尽可能重复利用水，尽量减少配料、原料和产品的溢、撒，清洗前总是先擦干净。

normal distribution

normal distributionnormal distribution, also called gaussian distribution, the most mon distribution function for independent, randomly generated variables. its familiar bell-shaped curve is ubiquitous in statistical reports, fromsurvey analysis and quality control to resource allocation.the graph of the normal distribution is characterized by two parameters: the mean, or average, which is the maximum of the graph and about which the graph is always symmetric; and the standard deviation, which determines the amount of dispersion away from the mean.a small standard deviation (pared with the mean) produces a steep graph, whereas a large standard deviation (again pared with the mean) produces a flat graph. see the figure.the normal distribution is produced by the normal density function, p(x) = e−(x−μ)2/2σ2/σsquare rootof√2π. in this exponential function e is the constant 2.71828…, is the mean, and σ is the standard deviation. the probability of a random variablefalling within any given range of values is equal to the proportion of the area enclosed under thefunction’s graph between the given values and above the x-axis. because the denominator (σsquare rootof√2π), known as the normalizing coefficient, causes the total area enclosed by the graph to be exactly equal to unity, probabilities can be obtained directlyfrom the corresponding area—i.e., an area of 0.5 corresponds to a probability of 0.5. although these areas can be determined with calculus, tables were generated in the 19th century for the special caseof = 0 and σ= 1, known as the standard normal distribution, and these tables can be used for any normal distribution after the variables are suitably rescaled by subtracting their mean and dividing by their standard deviation, (x−μ)/σ. calculators have now all but eliminated the use of such tables.for further details see probability theory.the term “gaussian distribution” refers to the german mathematician carl friedrich gauss, who first developed a two-parameter exponential function in 1809 in connection with studies of astronomical observation errors. this study led gauss to formulate his law of observational error and to advance the theory of the method of least squares approximation. another famous early application of the normal distribution was by the british physicist james clerk maxwell, who in 1859 formulated his law of distribution of molecular velocities—later generalized as the maxwell-boltzmann distribution law.the french mathematician abraham de moivre, in his doctrine of chances (1718), first noted that probabilities associated with discretely generated random variables (such as are obtained by flipping a coin or rolling a die) can be approximated by the area under the graph of an exponential function. thisresult was extended and generalized by the frenchscientist pierre-simon laplace, in his théorie analytique des probabilités(1812; “analytic theory of probability”), into the first central limit theorem, which proved that probabilities for almostall independent and identically distributed random variables converge rapidly (with sample size) to the area under an exponential function—that is, to a normal distribution. the central limit theorem permitted hitherto intractable problems, particularly those involving discrete variables, to be handled with calculus.。

统计词汇英语翻译

操作划定义：operational definition运算:operation全面调查：complete enumeration非全面调查：incomplete enumeration单变量：univariate多变量：multivariate变量层次：level of variable定序层次：nominal level定距层次：interval level定比层次：ratio level分布：distribution频次分布：frequency distribution集合：set of pairs变量值：value of variate相对频次分布：relative frequency distribution 完备:exhaustion互斥：mutual exclusion统计表：statistical tables连续型：continuous type离散型：discrete type组数：intervals等距：equal length非等距：unequal length精度：degree of accuracy分组点：limits标明组界：stated limits真实组界：true limits数据分组：grouping the data计算组距：class interval统计图：statistical graphs圆瓣图：Pie graphs条形图：bar graphs直方图：histograms相对频次密度：relative frequency density折线图：polygon累计图：cumulative graphs累计表：cumulative tables峰点：peak对称：symmetry左偏态或负向偏态: negatively skewed右偏态或正向偏态：positively skewedU形分布：U-shaped distributionJ--形分布：J-shaped distribution集中趋势：central tendency众值：Mode中位值：medium未分组数据：ungrouped data奇数：odd 偶数：even分组数据：grouped data上界：upper limit下界：lower limit上界累计百分数：upper cumulative percentage 下界累计百分数：lower cumulative percentage 均值：mean偏态：skewness异众比率：Variation ratio四分互差：interquartile range方差：variance标准差：standard variance归纳法：induction演绎法：deduction概率：probability随机现象：random phenomena不可能事件：impossible event可能结果：outcomes必然事件：sure (certain) event基本事件：elementary event样本空间：sample space样本点：sample point事件和：or conjunction事件积：as-well-as conjunction互不相容事件：mutually exclusive events对立事件：complementary events加法公式：addition rule乘法公式：multiplication rule相互独立：stochastically independent全概公式：total probabilities theorem概率分布：probability distribution离散型随机变量：discrete random variables连续型随机变量：continuous random variables 概率密度：probability density数学期望：expectation二项分布：binomial distribution二点分布： 2 points distribution排列：permutation组合：combinations多项分布：multinomial distribution超几何分布：hypergeometric distribution泊松分布：Poisson distribution正态分布：normal distribution标准分：standard scores大数定理：law of large numbers中心极限定理：central limit theorem统计推论：statistical inference参数估计：parameter estimation假设检验：hypothesis test总体：population样本：sample简单随即样本：simple random sample统计量：statistics点估计：point estimation最小方差：minimum variance抽样分布：sampling distribution区间估计：interval estimation显著性水平：significance level置信区间：confidence interval置信度：confidence coefficient原假设：hull hypothesis备择假设：alternative hypothesis单边检验：one-tailed test双边检验：two-tailed test假定：assumptions统计量：statistics临界值：critical value接受域：acceptance regions拒绝域：rejection regions两类错误：two types of error大样本：large sample小样本：small-sample独立样本：independent sample配对样本：paired sample联合分布：joint distribution边缘分布：marginal distribution期望频次：expected frequencies相关：association减少误差比例：proportional reduction in error等级相关：rank correlation斯皮尔曼等级相关：Spearmam’s rank order correlation 同序对：same ordered pair异序对：different ordered pair同分对：tied pairs回归：regression散步图：scattergram最小二乘法: least-squares criterion相关：correlation相关系数：coefficient of correlation预测：prediction方差分析：analysis of variance一元方差分析：one-way analysis of variance等方差性：equal variance相关比率：correlation ratio二元方差分析：two-way analysis of variance多元方差分析：multiple-way analysis of variance非参数检验：nonparametric tests符号检验：sign test符号秩检验：signed-rank test游程检验：run test累计频次检验：cumulative frequency test单向方向秩：one-way analysis of variance-rank双向方差秩：two-way analysis of variance-rank简单随机抽样：simple random sampling简单重复抽样：simple sampling with replacement简单不重复抽样：simple sampling without replacement 等距抽样：systematic sampling分层抽样：stratified sampling整群抽样：cluster sampling阶段抽样：multistage sampling样本容量：sample size。

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Max 77 55 54 11 28 28 11 2.53 2.03 2.07 1.99 .49 .97 .37
5th perc 4 1 0 0 1 1 0 .04 .01 .00 .00 .00 .01 .00
95th perc 67 53 52 5 23 22 4 1.50 1.27 1.92 .95 .36 .57 .11
imp-GER parameters at 5cm above LES
Total number of imp-GER (Z5) Total number acid imp-GER (Z5) Upright number acid imp-GER (Z5) Recumbent number acid imp-GER (Z5) Total number non-acid GER (Z5) Upight number non-acid imp-GER (Z5) Recumbent number non-acid imp-GER (Z5) Total percent time imp-GER (Z5) Total percent time acid imp-GER (Z5) Upright percent time acid imp-GER (Z5) Supine percent time acid imp-GER (Z5) Total percent time non-acid imp-GER (Z5) Upright percent time non-acid imp-GER (Z5) Supine percent time non-acid imp-GER (Z5) Mean 33 22 21 1 11 10 1 .61 .45 .64 .11 .15 .23 .03 SD 20 17 16 2 7 7 2 .47 .40 .54 .33 .12 .20 .08 Median 29 18 17 0 8 8 0 .48 .34 .51 .02 .11 .17 .00 Min 3 0 0 0 1 1 0 .04 .00 .00 .00 .00 .00 .00 Max 83 65 62 11 30 28 14 2.63 2.14 2.15 2.13 .50 .97 .54 5th perc 6 2 1 0 2 2 0 .05 .02 .03 .00 .02 .03 .00 95th perc 78 58 56 6 27 24 5 1.58 1.15 1.79 .99 .46 .68 .17
imp-GER parameters at 15cm above LES
Page 2
Total number of imp-GER (Z2) Total number acid imp-GER (Z2) Upright number acid imp-GER (Z2) Recumbent number acid imp-GER (Z2) Total number non-acid GER (Z2) Upight number non-acid imp-GER (Z2) Recumbent number non-acid imp-GER (Z2) Total percent time imp-GER (Z2) Total percent time acid imp-GER (Z2) Upright percent time acid imp-GER (Z2) Supine percent time acid imp-GER (Z2) Total percent time non-acid imp-GER (Z2) Upright percent time non-acid imp-GER (Z2) Supine percent time non-acid imp-GER (Z2)
pH GER parameters at 5cm above LES
Mean Total number of pH-GER Total number upright pH-GER Total number recumbent pH-GER Total percent time pH<4 Upright percent time pH<4 Recumbent percent time pH<4 17 16 1 1.67 2.43 .44 SD 14 13 2 1.90 3.20 1.00 Median 14 13 1 1.16 1.38 .03 Min 0 0 0 .00 .00 .00 Max 52 52 7 7.70 16.71 5.52 5th perc 0 0 0 .00 .00 .00 95th perc 48 46 6 7.04 11.20 3.19
Mean 13 9 9 1 4 3 0 .18 .16 .21 .06 .03 .04 .00
SD 13 10 9 1 4 4 1 .31 .28 .37 .25 .05 .08 .01
Median 8 6 5 0 2 2 0 .07 .04 .06 .00 .01 .01 .00
Min 0 0 0 0 0 0 0 .00 .00 .00 .00 .00 .00 .00
imp-GER parameters at 17cm above LES
Total number of imp-GER (Z1) Total number acid imp-GER (Z1) Upright number acid imp-GER (Z1) Recumbent number acid imp-GER (Z1) Total number non-acid GER (Z1) Upight number non-acid imp-GER (Z1) Recumbent number non-acid imp-GER (Z1) Total percent time imp-GER (Z1) Total percent time acid imp-GER (Z1) Upright percent time acid imp-GER (Z1) Supine percent time acid imp-GER (Z1) Total percent time non-acid imp-GER (Z1) Upright percent time non-acid imp-GER (Z1) Supine percent time non-acid imp-GER (Z1) Mean 11 8 7 1 3 3 0 .14 .12 .16 .03 .02 .03 .00 SD 12 9 9 1 4 4 0 .23 .20 .29 .16 .05 .07 .02 Median 6 4 4 0 2 2 0 .04 .02 .03 .00 .01 .00 .00 Min 0 0 0 0 0 0 0 .00 .00 .00 .00 .00 .00 .00 Max 68 47 46 8 21 20 2 1.21 1.18 1.70 1.19 .27 .38 .12 5th perc 0 0 0 0 0 0 0 .00 .00 .00 .00 .00 .00 .00 95th perc 36 29 23 3 10 10 1 .73 .59 .77 .23 .19 .30 .05
Mean 28 19 18 1 9 8 1 .51 .39 .56 .10 .11 .17 .02
Байду номын сангаас
SD 19 16 15 2 7 6 2 .46 .39 .53 .31 .11 .18 .05
Median 23 15 14 0 6 6 0 .38 .29 .42 .00 .09 .11 .00
Min 3 0 0 0 0 0 0 .01 .00 .00 .00 .00 .00 .00
Max 72 50 50 9 22 21 3 1.51 1.47 2.13 1.58 .26 .40 .06
5th perc 0 0 0 0 0 0 0 .00 .00 .00 .00 .00 .00 .00
95th perc 39 33 27 3 15 14 1 1.18 .94 1.05 .59 .15 .25 .04
imp-GER parameters at 7cm above LES
Page 1
Total number of imp-GER (Z4) Total number acid imp-GER (Z4) Upright number acid imp-GER (Z4) Recumbent number acid imp-GER (Z4) Total number non-acid GER (Z4) Upight number non-acid imp-GER (Z4) Recumbent number non-acid imp-GER (Z4) Total percent time imp-GER (Z4) Total percent time acid imp-GER (Z4) Upright percent time acid imp-GER (Z4) Supine percent time acid imp-GER (Z4) Total percent time non-acid imp-GER (Z4) Upright percent time non-acid imp-GER (Z4) Supine percent time non-acid imp-GER (Z4)
imp-GER parameters at 3 cm above LES
Total number of imp-GER (Z6) Total number acid imp-GER (Z6) Upright number acid imp-GER (Z6) Recumbent number acid imp-GER (Z6) Total number non-acid GER (Z6) Upight number non-acid imp-GER (Z6) Recumbent number non-acid imp-GER (Z6) Total percent time imp-GER (Z6) Total percent time acid imp-GER (Z6) Upright percent time acid imp-GER (Z6) Supine percent time acid imp-GER (Z6) Total percent time non-acid imp-GER (Z6) Upright percent time non-acid imp-GER (Z6) Supine percent time non-acid imp-GER (Z6) Mean 33 22 21 1 11 10 1 .69 .51 .72 .12 .18 .27 .04 SD 20 17 16 2 7 7 2 .50 .43 .57 .34 .13 .22 .09 Median 29 18 17 0 8 8 0 .56 .41 .58 .02 .14 .20 .00 Min 3 0 0 0 1 1 0 .04 .00 .00 .00 .01 .02 .00 Max 83 65 62 11 30 28 14 2.77 2.26 2.31 2.20 .55 1.01 .60 5th perc 6 2 1 0 2 2 0 .09 .05 .07 .00 .02 .04 .00 95th perc 78 58 56 6 27 24 5 1.61 1.16 1.73 1.00 .51 .78 .20